Tootfinder

#DanDaDan second season is getting closer and I'm excited!

The Unit-Zero Divisor Graph of a Commutative Ring
Vika Yugi Kurniawan, Yeni Susanti, Budi Surodjo
https://arxiv.org/abs/2506.11495 https://

The Unit-Zero Divisor Graph of a Commutative Ring
This paper introduces a new approach to associating a graph with a commutative ring. Let $R$ be a commutative ring with identity. The unit-zero divisor graph of a commutative ring $R$, denoted by $G_{UZ}(R)$, offers a novel framework for exploring the interaction between ring and graph structures. The vertex set of $G_{UZ}(R)$ consists of all elements of the ring $R$. Two distinct vertices $x$ and $y$ in $G_{UZ}(R)$ are adjacent if and only if $x + y$ is a unit and $xy$ is a zero divisor in $R$…

Google services, AWS, Spotify, Cloudflare, and other services appear to be in a partial outage, according to Downdetector (Ben Schoon/9to5Google)
https://9to5google.com/2025/06/12/google-cloud-outage-june-12/

It’s not just you, Google and many other web services appear to be in a partial outage right now
If you’re struggling with Google services right now, you’re not alone as it appears that a partial outage is affecting...

🇺🇦 #NowPlaying on KEXP's #VarietyMix
Samthing Soweto, De Mthuda & Njelic:
🎵 Chomi (feat. Njelic)
#SamthingSoweto #DeMthuda #Njelic
https://open.spotify.com/track/5gPf9DPJpohxdAxcN3q9rN

@… willkommen zurück! 👋

This https://arxiv.org/abs/2503.02768 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csPL_…

Denotational Semantics for Probabilistic and Concurrent Programs
We develop a denotational model for probabilistic and concurrent imperative programs, a class of programs with standard control flow via conditionals and while-loops, as well as probabilistic actions and parallel composition. Whereas semantics for concurrent or randomized programs in isolation is well studied, their combination has not been thoroughly explored and presents unique challenges. The crux of the problem is that interactions between control flow, probabilistic actions, and concurrent…

"Rubber" bullets
https://www.reddit.com/r/Damnthatsinteresting/comments/uxnnt0/steel_core_inside_of_a_rubber_bullet_used_by/

Cycles and paths through vertices whose degrees are at least the bipartite-hole-number
Chengli Li, Feng Liu, Yurui Tang
https://arxiv.org/abs/2506.09750 ht…

Cycles and paths through vertices whose degrees are at least the bipartite-hole-number
The bipartite-hole-number of a graph $G$, denoted by $\widetildeα(G)$, is the minimum integer $k$ such that there exist positive integers $s$ and $t$ with $s + t = k + 1$, satisfying the property that for any two disjoint sets $A, B \subseteq V(G)$ with $|A| = s$ and $|B| = t$, there is at least one edge between $A$ and $B$. In 1992, Bollobás and Brightwell, and independently Shi, proved that every $2$-connected graph of order $n$ contains a cycle passing through all verti…

Betrieb an wichtigen Moskauer Flughäfen ausgesetzt
Die zivile russische Luftfahrtbehörde (Rosaviatia) hat angesichts eines ukrainischen Drohnenangriffs am Morgen den Betrieb an zwei wichtigen internationalen Moskauer Flughäfen vorläufig gestoppt. Flüge in Wnukowo und Domodedowo wurden demnach aus Sicherheitsgründen ausgesetzt. Die Flugabwehr habe neun ukrainische Drohnen mit Kurs Moskau zerstört, teilte der Bürgermeister der …
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Ukraine-Liveblog: ++ Selenskyj: Putin will totale Niederlage der Ukraine ++
Kremlchef Putin ist nach Meinung des ukrainischen Präsidenten Selenskyj nicht an einem Waffenstillstand interessiert. Bei russischen Angriffen wurde nach ukrainischen Angaben in der Region Dnipropetrowsk mindestens ein Mensch getötet. Der Liveblog vom Sonntag zum Nachlesen.

Proof of a conjecture on isolation of graphs with a universal vertex
Peter Borg, Alastair Farrugia
https://arxiv.org/abs/2506.09290 https://

Proof of a conjecture on isolation of graphs with a universal vertex
A copy of a graph $F$ is called an $F$-copy. For any graph $G$, the $F$-isolation number of $G$, denoted by $ι(G,F)$, is the size of a smallest subset $D$ of the vertex set of $G$ such that the closed neighbourhood $N[D]$ of $D$ in $G$ intersects the vertex sets of the $F$-copies contained by $G$ (equivalently, $G-N[D]$ contains no $F$-copy). Thus, $ι(G,K_1)$ is the domination number $γ(G)$ of $G$, and $ι(G,K_2)$ is the vertex-edge domination number of $G$. Settling a conjecture of Zhang an…