Tootfinder

Hey, Jörg Schoppmeyer opened his talk at the #SolarEclipse Conference in Leuven on imaging annular eclipses without filters with one of my Australian pictures from 1999 (upper right): see https://geocities.restorativland.org/CapeCanaveral/5599/aus99/story.html for how they originated. Schoppmeyer's video https://www.youtube.com/watch?v=lbtQrHdl5Og of the 2023 ASE actually found scientific use: https://www.iota-es.de/JOA/JOA2024_2.pdf#page=3 (once again confirming the larger solar diameter https://scicomm.xyz/@cosmos4u/114681336115327260 had determined by an entirely different technique). 6/n

A note on the properties of the confidence set for the local average treatment effect obtained by inverting the score test
Ezequiel Smucler, Ludovico Lanni, David Masip
https://arxiv.org/abs/2506.10449

A note on the properties of the confidence set for the local average treatment effect obtained by inverting the score test
We study the properties of the score confidence set for the local average treatment effect in non and semiparametric instrumental variable models. This confidence set is constructed by inverting a score test based on an estimate of the nonparametric influence function for the estimand, and is known to be uniformly valid in models that allow for arbitrarily weak instruments; because of this, the confidence set can have infinite diameter at some laws. We characterize the six possible forms the sc…

Torus covers with controlled volume and diameter
Sergio Zamora
https://arxiv.org/abs/2506.00763 https://arxiv.org/pdf/2506.00763

Torus covers with controlled volume and diameter
We show that under a lower Ricci curvature bound and an upper diameter bound, a torus admits a finite-sheeted covering space with volume bounded from below and diameter bounded from above. This partially recovers a result of Kloeckner and Sabourau, whose original proof contains a serious gap that currently lacks a resolution.

A characterization of all graphs cospectral to the double star $P_2(1,n)$
Emily Barranca, Michael D. Barrus
https://arxiv.org/abs/2506.06934 https://

A characterization of all graphs cospectral to the double star $P_2(1,n)$
We examine the adjacency spectrum of trees with diameter three, also referred to as double stars. Using $P_2(a,b)$ to denote a double star with $ a$ and $b$ leaves at its respective endpoints, we discuss graphs which are cospectral to double stars for various parameters $a$ and $b$. In particular, we give constructions for graphs cospectral to $P_2(1,2k)$ for integers $k$. Lastly, we show that the double star $P_2(1,n)$ is determined by its spectrum when $n$ is odd. That is, if a graph $G$ cosp…

Euclid preparation: The NISP spectroscopy channel, on ground performance and calibration
Collaboration, Gillard, Maciaszek, Prieto, Grupp, Costille, Jahnke, Clemens, Dusini, Carle, Sirignano, Medinaceli, Ligori, Franceschi, Trifoglio, Bon, Barbier, Ferriol, Secroun, Auricchio, Battaglia, Bonoli, Corcione, Hormuth, Le Mignant, Morgante, Padilla, Toledo-Moreo, Valenziano, Bender, Castander, Lilje, Balestra, Barriere, Berthe, Boderndorf, Bonnefoi, Capobianco, Casas, Cho, Ducret, Gimenez, …

Euclid preparation: The NISP spectroscopy channel, on ground performance and calibration
ESA's Euclid cosmology mission relies on the very sensitive and accurately calibrated spectroscopy channel of the Near-Infrared Spectrometer and Photometer (NISP). With three operational grisms in two wavelength intervals, NISP provides diffraction-limited slitless spectroscopy over a field of $0.57$ deg$^2$. A blue grism $\text{BG}_\text{E}$ covers the wavelength range $926$--$1366$\,nm at a spectral resolution $R=440$--$900$ for a $0.5''$ diameter source with a dispersion of $1.24$ nm px$^{-1…

Visible Brillouin-quadratic microlaser in a high-Q thin-film lithium niobate microdisk
Xiaochao Luo, Chuntao Li, Xingzhao Huang, Jintian Lin, Renhong Gao, Yifei Yao, Yingnuo Qiu, Yixuan Yang, Lei Wang, Huakang Yu, Ya Cheng
https://arxiv.org/abs/2506.08615

Visible Brillouin-quadratic microlaser in a high-Q thin-film lithium niobate microdisk
Narrow-linewidth lasers at short/visible wavelengths are crucial for quantum and atomic applications, such as atomic clocks, quantum computing, atomic and molecular spectroscopy, and quantum sensing. However, such lasers are often only accessible in bulky tabletop systems and remain scarce in integrated photonic platform. Here, we report an on-chip visible Brillouin-quadratic microlaser in a 117-um-diameter thin-film lithium niobate (TFLN) microdisk via dispersion engineering. Enabled by the ul…

A Combinatorial Approach to Novel Boundary Design in Deterministic Lateral Displacement
Aryan Mehboudi, Shrawan Singhal, S. V. Sreenivasan
https://arxiv.org/abs/2506.06936

A Combinatorial Approach to Novel Boundary Design in Deterministic Lateral Displacement
Deterministic lateral displacement (DLD) is a high-resolution separation technique used in various fields. A fundamental challenge in DLD is ensuring uniform flow characteristics across channel, particularly near sidewalls where pillar matrix inevitably loses its lateral periodicity. Despite attempts in the literature to improve boundary design, significant variations in critical diameter persist near sidewalls, adversely affecting the separation performance. We propose a combinatorial framewor…

Thermodynamics and Shadows of Kerr black holes endowed with a global monopole charge
Balendra Pratap Singh, Md Sabir Ali
https://arxiv.org/abs/2506.02653 h…

Thermodynamics and Shadows of Kerr black holes endowed with a global monopole charge
In this article, we present the thermodynamic and shadow properties of rotating black holes with global monopole charge. The angular diameter of Sgr A$^{*}$ black hole is 48.7 $\pm$ 7 $μas$, which is 8 $kps$ far away having a mass of $M = 4.0_{-0.6}^{+1.1} \times 10^6 M\odot$ as observed by Event Horizon Telescope and for the M87 black hole, the observed angular diameter is $θ_d = 42 \pm 3 μ$as, which is almost $16$ $Mpc$ far away with a mass of $M = (6.5 \pm 0.7) \times 10^9 M_\odot$. The g…

Acoustic-Driven Surface Cleaning with Millimeter-Sized Bubbles at Translational Resonance
Yan Jun Lin, Zhengyang Liu, Sunghwan Jung
https://arxiv.org/abs/2506.06581

Acoustic-Driven Surface Cleaning with Millimeter-Sized Bubbles at Translational Resonance
Traditional surface cleaning methods often suffer from drawbacks such as chemical harshness, potential for surface damage, and high energy consumption. This study investigates an alternative approach: acoustic-driven surface cleaning using millimeter-sized bubbles excited at low, sub-cavitation frequencies. We identify and characterize a distinct translational resonance of these bubbles, occurring at significantly lower frequencies (e.g., 50 Hz for 1.3 mm diameter bubbles) than the Minnaert res…

Very interesting talks at the #SolarEclipse Conference - https://www.vvs.be/subsite/sec-2025/programme - in Belgium I am attending online: here is the key result by Luca Quaglia who had reported his work in great detail in the papers https://iopscience.iop.org/article/10.3847/1538-4365/ac1279 (2021), https://www.iota-es.de/JOA/JOA2022_2.pdf#page=3 (2022) and https://www.iota-es.de/JOA/JOA2024_4.pdf#page=3 (2024) already. There seems to be NO way by now to escape the conclusion the the solar - i.e. photospheric - diameter used by many in the past (and various eclipse map calculations sites still today) is too small. So everyone should use Quaglia's free precision tools at https://www.besselianelements.com instead to get the real length of totality at one's observing spot. And when you are observing at the edges of the totality zone the tools will tell you where the actual border is: traditional maps can the off by some margin! 1/n

Nilpotent graphs over skew PBW extensions
Sebasti\'an Higuera, Armando Reyes
https://arxiv.org/abs/2506.00632 https://arxiv.org/p…

Nilpotent graphs over skew PBW extensions
We investigate the diameter and girth of the nilpotent graph for skew PBW extensions over $2$-primal rings, generalizing similar results on skew polynomial rings. Under certain compatibility conditions, we establish bounds for the diameter of the nilpotent graph and prove invariance of the girth under polynomial extensions.

Low-temperature cotunneling electron transport in photo-switchable molecule-nanoparticle networks
Yannick Viero, David Gu\'erin, Dominique Vuillaume
https://arxiv.org/abs/2506.05552

Low-temperature cotunneling electron transport in photo-switchable molecule-nanoparticle networks
We report the temperature-dependent (4.2 - 300 K) electron transport properties (current-voltage) of photo-switchable two-dimensional arrays of gold nanoparticles (10 nm in diameter) functionalized by azobenzene derivatives. Under UV-light irradiation at 4.2 K, the azobenzene moieties are switched from the trans to cis isomers, leading to an increase of the current. In both conformations, at low temperature (< 77 K) and low voltage (< 1 V) the voltage- and temperature-dependent current behavior…

Thirty-Three New Stellar Angular Diameters from the NPOI, and Nearly 180 NPOI Diameters as an Ensemble
Ellyn K. Baines, James H. Clark III, Henrique R. Schmitt, Jordan M. Stone, Kaspar von Braun
https://arxiv.org/abs/2505.23514

Thirty-Three New Stellar Angular Diameters from the NPOI, and Nearly 180 NPOI Diameters as an Ensemble
We present new angular diameter measurements for 33 stars from the Navy Precision Optical Interferometer, reaching uncertainties on the limb-darkened diameter of 2% or less for 21 targets. We also determined the physical radius, bolometric flux, luminosity, and effective temperature for each star. Our sample is a mix of giant, subgiant, and dwarf stars, and span spectral classes from mid-A to to mid-K. We combined these 33 stars with samples from previous publications to analyze how the NPOI di…

Vaccinium myrtillus, Blåbær i blomstring, European. blueberry flowering.
#BloomScrolling

Fully-Distributed Construction of Byzantine-Resilient Dynamic Peer-to-Peer Networks
Aayush Gupta, Gopal Pandurangan
https://arxiv.org/abs/2506.04368 https:…

Fully-Distributed Construction of Byzantine-Resilient Dynamic Peer-to-Peer Networks
We address a fundamental problem in Peer-to-Peer (P2P) networks, namely, constructing and maintaining dynamic P2P overlay network topologies with essential properties such as connectivity, low diameter, and high expansion, that are resilient to continuous high churn and the presence of a large number of malicious (Byzantine) nodes. Our main goal is to construct and maintain a sparse (bounded degree) expander topology despite high churn and a large number of Byzantine nodes. Such an expander top…

[T]he earliest radio shows are on the surface of an electromagnetic sphere now 200 light-years in diameter, a sphere expanding at the speed of light. If there is intelligence "out there," looking for signs of intelligent life in the cosmos, its first knowledge of humans will come from (probably) Amos 'n' Andy. Now that is, indeed, a sobering, even disquieting thought.
- Paul J. Nahin, The Mathematical Radio: Inside the Magic of AM, FM, and Single-Sideband

Small area estimation of growing stock timber volume, basal area, mean stem diameter, and stem density for mountain forests in Austria
Arne Nothdurft, Valentin Sarkleti, Tobias Ofner-Graff, Andreas Tockner, Christoph Gollob, Tim Ritter, Ralf Kra{\ss}nitzer, Philip Svazek, Martin K\"uhmaier, Karl Stampfer, Andrew O. Finley
https://

Small area estimation of growing stock timber volume, basal area, mean stem diameter, and stem density for mountain forests in Austria
Regression models were evaluated to estimate stand-level growing stock volume (GSV), quadratic mean diameter (QMD), basal area (BA), and stem density (N) in the Brixen im Thale forest district of Austria. Field measurements for GSV, QMD, and BA were collected on 146 inventory plots using a handheld mobile personal laser scanning system. Predictor variables were derived from airborne laser scanning (ALS)-derived normalized digital surface and terrain models. The objective was to generate stand-l…

Spectral convergence of graph Laplacians with Ricci curvature bounds and in non-collapsed Ricci limit spaces
Masato Inagaki
https://arxiv.org/abs/2506.07427

Spectral convergence of graph Laplacians with Ricci curvature bounds and in non-collapsed Ricci limit spaces
This paper establishes quantitative high-probability bounds on the eigenvalues and eigenfunctions of $ε$-neighborhood graph Laplacians constructed from i.i.d. random variables on $m$-dimensional closed Riemannian manifolds $(M,g)$ that satisfy a uniform lower Ricci curvature bound $\operatorname{Ric}_g\ge -(m-1)K$, a positive lower volume bound, and an upper diameter bound. These results extend to non-collapsed Ricci limit spaces that are measured Gromov-Hausdorff limits of such manifolds, and…

This https://arxiv.org/abs/2408.03465 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCC_…

Algorithms for the Diverse-k-SAT problem: the geometry of satisfying assignments
Given a $k$-CNF formula and an integer $s$, we study algorithms that obtain $s$ solutions to the formula that are maximally dispersed. For $s=2$, the problem of computing the diameter of a $k$-CNF formula was initiated by Creszenzi and Rossi, who showed strong hardness results even for $k=2$. Assuming SETH, the current best upper bound [Angelsmark and Thapper '04] goes to $4^n$ as $k \rightarrow \infty$. As our first result, we give exact algorithms for using the Fast Fourier Transform and cliq…

Vietoris--Rips Shadow for Euclidean Graph Reconstruction
Rafal Komendarczyk, Sushovan Majhi, Atish Mitra
https://arxiv.org/abs/2506.01603 https://

Vietoris--Rips Shadow for Euclidean Graph Reconstruction
The shadow of an abstract simplicial complex $K$ with vertices in $\mathbb R^N$ is a subset of $\mathbb R^N$ defined as the union of the convex hulls of simplices of $K$. The Vietoris--Rips complex of a metric space $(S,d)$ at scale $β$ is an abstract simplicial complex whose each $k$-simplex corresponds to $(k+1)$ points of $S$ within diameter $β$. In case $S\subset\mathbb R^2$ and $d(a,b)=\|a-b\|$ standard Euclidean, the natural shadow projection of the Vietoris--Rips is already p…

This https://arxiv.org/abs/2404.11389 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finding $d$-Cuts in Graphs of Bounded Diameter, Graphs of Bounded Radius and $H$-Free Graphs
The $d$-Cut problem is to decide if a graph has an edge cut such that each vertex has at most $d$ neighbours at the opposite side of the cut. If $d=1$, we obtain the intensively studied Matching Cut problem. The $d$-Cut problem has been studied as well, but a systematic study for special graph classes was lacking. We initiate such a study and consider classes of bounded diameter, bounded radius and $H$-free graphs. We prove that for all $d\geq 2$, $d$-Cut is polynomial-time solvable for graphs …

Investigating the HI distribution and kinematics of ESO444-G084 and [KKS2000]23: New insights from the MHONGOOSE survey
Brenda Namumba, Roger Ianjamasimanana, B\"arbel Koribalski, Albert Bosma, Evangelia Athanassoula, Claude Carignan, Gyula I. G. J\'ozsa, Peter Kamphuis, Roger P. Deane, Sinenhlanhla P. Sikhosana, Lourdes Verdes-Montenegro, Amidou Sorgho, Xola Ndaliso, Philippe Amram, Elias Brinks, Laurent Chemin, Francoise Combes, Erwin de Blok, Nathan Deg, Jayanne English, Ju…

Investigating the HI distribution and kinematics of ESO444-G084 and [KKS2000]23: New insights from the MHONGOOSE survey
We present the HI distribution, kinematics, mass modeling, and disk stability of the dwarf irregular galaxies ESO444-G084 and [KKS2000]23 using high-resolution, high-sensitivity MHONGOOSE survey data from MeerKAT. ESO444-G084 shows centrally concentrated HI emission, while [KKS2000]23 exhibits irregular high-density clumps. Total HI fluxes measured down to 10^19 and 10^18 cm^-2 are nearly identical, indicating that the increased HI diameter at lower column densities results mainly from the larg…

Probing Cosmic Curvature with Fast Radio Bursts and DESI DR2
J\'eferson A. S. Fortunato, Wiliam S. Hip\'olito-Ricaldi, Gustavo E. Romero
https://arxiv.org/abs/2506.01504

Probing Cosmic Curvature with Fast Radio Bursts and DESI DR2
The spatial curvature of the Universe remains a central question in modern cosmology. In this work, we explore the potential of localized Fast Radio Bursts (FRBs) as a novel tool to constrain the cosmic curvature parameter $Ω_k$ in a cosmological model-independent way. Using a sample of 80 FRBs with known redshifts and dispersion measures, we reconstruct the Hubble parameter $H(z)$ via artificial neural networks, which is then used to obtain angular diameter distances $D_A(z)$ through two comp…

On the shape of the typical Poisson-Voronoi cell in high dimensions
Matthias Irlbeck, Zakhar Kabluchko, Tobias M\"uller
https://arxiv.org/abs/2506.02607

On the shape of the typical Poisson-Voronoi cell in high dimensions
We study the typical cell of the Poisson-Voronoi tessellation. We show that when divided by the $d$-th root of the intensity parameter $λ$ of the Poisson process times the volume of the unit ball, the inradius, outradius, diameter and mean width of the typical cell converge in probability to the constants $1/2, 1, 2, 2$ respectively, as the dimension $d\to\infty$. We also show that the width of the typical cell, when rescaled in the same way, is bounded between $2\sqrt{5}/(2+\sqrt{5})-o_d(1)$ …

Observation of the Crab Nebula with the Single-Mirror Small-Size Telescope stereoscopic system at low altitude
C. Alispach, A. Araudo, M. Balbo, V. Beshley, J. Bla\v{z}ek, J. Borkowski, S. Boula, T. Bulik, F. Cadoux, S. Casanova, A. Christov, J. Chudoba, L. Chytka, P. \v{C}echvala, P. D\v{e}dic, D. della Volpe, Y. Favre, M. Garczarczyk, L. Gibaud, T. Gieras, E. G{\l}owacki, P. Hamal, M. Heller, M. Hrabovsk\'y, P. Jane\v{c}ek, M. Jel\'inek, V. J\'ilek, J. Jury\v{s}ek, V. Kar…

Observation of the Crab Nebula with the Single-Mirror Small-Size Telescope stereoscopic system at low altitude
The Single-Mirror Small-Size Telescope (SST-1M) stereoscopic system is composed of two Imaging Atmospheric Cherenkov Telescopes (IACTs) designed for optimal performance for gamma-ray astronomy in the multi-TeV energy range. It features a 4-meter-diameter tessellated mirror dish and an innovative SiPM-based camera. Its optical system features a 4-m diameter spherical mirror dish based on the Davies-Cotton design, maintaining a good image quality over a large FoV while minimizing optical aberrati…

This https://arxiv.org/abs/2502.03663 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

Fast Geographic Routing in Fixed-Growth Graphs
In the 1960s, the social scientist Stanley Milgram performed his famous "small-world" experiments where he found that people in the US who are far apart geographically are nevertheless connected by remarkably short chains of acquaintances. Since then, there has been considerable work to design networks that accurately model the phenomenon that Milgram observed. One well-known approach was Barab{á}si and Albert's preferential attachment model, which has small diameter yet lacks an algorithm tha…

A Start To End Machine Learning Approach To Maximize Scientific Throughput From The LCLS-II-HE
Aashwin Mishra, Matt Seaberg, Ryan Roussel, Fred Poitevin, Jana Thayer, Daniel Ratner, Auralee Edelen, Apurva Mehta
https://arxiv.org/abs/2505.23858

A Start To End Machine Learning Approach To Maximize Scientific Throughput From The LCLS-II-HE
With the increasing brightness of Light sources, including the Diffraction-Limited brightness upgrade of APS and the high-repetition-rate upgrade of LCLS, the proposed experiments therein are becoming increasingly complex. For instance, experiments at LCLS-II-HE will require the X-ray beam to be within a fraction of a micron in diameter, with pointing stability of a few nanoradians, at the end of a kilometer-long electron accelerator, a hundred-meter-long undulator section, and tens of meters l…

On generalized limits and ultrafilters
Paolo Leonetti, Cihan Orhan
https://arxiv.org/abs/2505.23263 https://arxiv.org/pdf/2505.23263

On generalized limits and ultrafilters
Given an ideal $\mathcal{I}$ on $ω$, we denote by $\mathrm{SL}(\mathcal{I})$ the family of positive normalized linear functionals on $\ell_\infty$ which assign value $0$ to all characteristic sequences of sets in $\mathcal{I}$. We show that every element of $\mathrm{SL}(\mathcal{I})$ is a Choquet average of certain ultrafilter limit functionals. Also, we prove that the diameter of $\mathrm{SL}(\mathcal{I})$ is $2$ if and only if $\mathcal{I}$ is not maximal, and that the latter claim can be co…

Geodesic transitive graphs of small valency
Jun-Jie Huang
https://arxiv.org/abs/2506.04670 https://arxiv.org/pdf/2506.04670

Geodesic transitive graphs of small valency
For a graph $Γ$, the {\em distance} $d_Γ(u,v)$ between two distinct vertices $u$ and $v$ in $Γ$ is defined as the length of the shortest path from $u$ to $v$, and the {\em diameter} $\mathrm{diam}(Γ)$ of $Γ$ is the maximum distance between $u$ and $v$ for all vertices $u$ and $v$ in the vertex set of $Γ$. For a positive integer $s$, a path $(u_0,u_1,\ldots,u_{s})$ is called an {\em $s$-geodesic} if the distance of $u_0$ and $u_s$ is $s$. The graph $Γ$ is said to be {\em distance transiti…

Optimizing SPION Labeling for Single-Cell Magnetic Microscopy
A. Pointner, D. Thalheim, S. Belasi, L. Heinen, C. Bonato, T. Luehmann, J. Meijer, R. Tietze, C. Alexiou, R. Schneider-Stock, R. Nagy
https://arxiv.org/abs/2505.20373

Optimizing SPION Labeling for Single-Cell Magnetic Microscopy
This study explores the correlation between iron mass on cell surfaces and the resultant magnetic field. Human colorectal cancer cells (HT29 line) were labeled with varying concentrations of SPIONs and imaged via a NV center widefield magnetic microscope. To assess the labeling efficacy, a convolutional neural network trained on simulated magnetic dipole data was utilized to reconstruct key labeling parameters on a cell-by-cell basis, including cell diameter, sensor proximity, and the iron mass…

This https://arxiv.org/abs/2402.19372 has been replaced.
initial toot: https://mastoxiv.page/@arX…

A miniaturized magnetic field sensor based on nitrogen-vacancy centers
The nitrogen-vacancy (NV) center in diamond is a prime candidate for quantum sensing technologies. Here, we present a fully integrated and mechanically robust fiber-based endoscopic sensor with a tip diameter of $1.25 \mathrm{mm}$. On its tip, a direct laser writing process is used to fixate a diamond containing NV centers above the fiber's core inside a polymer structure. Additionally, a metallic direct laser-written antenna structure next to the fiber facet allows efficient microwave manipula…

Jet breakup dynamics of viscoelastic carboxymethyl cellulose solutions
Ketan Vinayak Warghat, Yogesh Biswal, Sukesh Sharma, Pankaj Sharadchandra Kolhe, Lakshmana Dora Chandrala, Kirti Chandra Sahu
https://arxiv.org/abs/2506.00516

Jet breakup dynamics of viscoelastic carboxymethyl cellulose solutions
We experimentally investigate the breakup dynamics of viscoelastic jets composed of carboxymethyl cellulose (CMC) solutions, focusing on the dripping and Rayleigh regimes at low flow rates. By varying the CMC concentration, needle diameter ($D_n$), and flow rate ($Q$), we analyze the effects of elasticity, viscosity, and flow conditions on jet stability and droplet formation. Our results show that increasing CMC concentration enhances viscoelastic effects, leading to prolonged jet lifetimes, ex…

2-Homogeneous bipartite distance-regular graphs and the quantum group $U^\prime_q(\mathfrak{so}_6)$
Paul Terwilliger
https://arxiv.org/abs/2506.02190 https…

2-Homogeneous bipartite distance-regular graphs and the quantum group $U^\prime_q(\mathfrak{so}_6)$
We consider a 2-homogeneous bipartite distance-regular graph $Γ$ with diameter $D \geq 3$. We assume that $Γ$ is not a hypercube nor a cycle. We fix a $Q$-polynomial ordering of the primitive idempotents of $Γ$. This $Q$-polynomial ordering is described using a nonzero parameter $q \in \mathbb C$ that is not a root of unity. We investigate $Γ$ using an $S_3$-symmetric approach. In this approach one considers $V^{\otimes 3} = V \otimes V \otimes V$ where $V$ is the standard module of $Γ$. W…

Vulnerability Measures and Zagreb Indices of Graphs
Sanju Vaidya, Cheng Chang
https://arxiv.org/abs/2505.24707 https://arxiv.org/pdf/…

Vulnerability Measures and Zagreb Indices of Graphs
This paper establishes sharp bounds for the vulnerability measures of closeness and generalized closeness in graphs and identifies graphs that attain these bounds. It further develops bounds incorporating Zagreb indices for triangle- and quadrangle-free graphs, yielding formulas for closeness and generalized closeness in such graphs with diameter at most 3. Moreover, using Zagreb indices, we derive bounds for trees and connected graphs with girth at least 7, which are attained by graphs with di…