Tootfinder

Degree-similar graphs and cospectral graphs
Yi-Zheng Fan, Ruo-Jie Xing, Yi-Liu Zhang, Wei Wang
https://arxiv.org/abs/2509.01520 https://arxiv.org/pdf/2509.…

Degree-similar graphs and cospectral graphs
Let $G$ be a graph with adjacency matrix $A(G)$ and degree matrix $D(G)$, and let $L_μ(G):=A(G)-μD(G)$. Two graphs $G_1$ and $G_2$ are called \emph{degree-similar} if there exists an invertible matrix $M$ such that $M^{-1} A(G_1) M =A(G_2)$ and $M^{-1} D(G_1) M =D(G_2)$. In this paper, we address three problems concerning degree-similar graphs proposed by Godsil and Sun. First, we present a new characterization of degree-similar graphs using degree partition, from which we derive methods and …

»Der Hitze aus dem Weg gehen – "Vampir Modus" - An dieser Navigation hätte Dracula viel Freude:
Welcher Weg schützt mich vor Hitze? Antwort darauf hat eine neue, spezielle Fussgänger-Navigation der Fachhochschule Ost. Der "Vampir-Modus" berechnet dazu die schattigsten Routen«
Ich als Vampir habe nun das @… App was ich beim jet…

Der Hitze aus dem Weg gehen - «Vampir Modus»: An dieser Navigation hätte Dracula viel Freude
Welcher Weg schützt mich vor Hitze? Eine neue Fussgänger-Navigation, der «Vampir-Modus», kennt die schattigsten Routen.

Google setzt die KI-gestützte Suchfunktion "Ask Photos" vorerst aus
Mithilfe Geminis werden Nutzer die Fotos-App von Google durchsuchen können. Doch es gibt Probleme mit dieser Funktion. Google will in zwei Wochen nachbessern.

Gary H. came through again today.
#Bible

The Maximum Likelihood Degree of Toric Models is Monotonic
Carlos Am\'endola, Janike Oldekop, Maximilian Wiesmann
https://arxiv.org/abs/2507.02719 http…

The Maximum Likelihood Degree of Toric Models is Monotonic
We settle a conjecture by Coons and Sullivant stating that the maximum likelihood (ML) degree of a facial submodel of a toric model is at most the ML degree of the model itself. We discuss the impact on the ML degree from observing zeros in the data. Moreover, we connect this problem to tropical likelihood degenerations, and show how the results can be applied to discrete graphical and quasi-independence models.

🇺🇦 #NowPlaying on KEXP's #SundaySoul
Don Blackman:
🎵 Heart's Desire
#DonBlackman
https://breakfasttriple.bandcamp.com/track/don-blackman-hearts-desire-breakfast-triple-remix
https://open.spotify.com/track/5jpYsq5cYKeQDRgn8WTenS

The class divide among women in the workplace is widening (Emily Peck/Axios)
https://www.axios.com/2025/08/03/women-college-degree-jobs
http://www.memeorandum.com/250803/p18#a250803p18

The net-regular strongly regular signed graphs with degree 6
Qian Yu, Yaoping Hou
https://arxiv.org/abs/2508.00302 https://arxiv.org/pdf/2508.00302

The net-regular strongly regular signed graphs with degree 6
In this paper, we study the net-regular strongly regular signed graphs with degree 6 and determine all connected 6-regular and net-regular strongly regular signed graphs. There are three, six and four 6-regular strongly regular signed graphs with net-degree 4, 2 and 0, respectively.

Oriented Diameter of Mixed Graphs with Given Maximum Undirected Degree
Ran An, Hengzhe Li, Jianbing Liu, Gaoxing Sun
https://arxiv.org/abs/2507.02277 https…

Oriented Diameter of Mixed Graphs with Given Maximum Undirected Degree
In 2018, Dankelmann, Gao, and Surmacs [J. Graph Theory, 88(1): 5--17, 2018] established sharp bounds on the oriented diameter of a bridgeless undirected graph and a bridgeless undirected bipartite graph in terms of vertex degree. In this paper, we extend these results to \emph{mixed graphs}, which contain both directed and undirected edges. Let the \emph{undirected degree} $d^*_G(x)$ of a vertex $x \in V(G)$ be the number of its incident undirected edges in a mixed graph $G$ of order $n$, and…