A graph is said to be walk-regular if, for each $\ell \geq 1$, every vertex is contained in the same number of closed walks of length $\ell$. We construct a $24$-vertex graph $H_4$ that is not walk-regular yet has maximized walk entropy, $S^V(H_4,β)...
We prove a sharpened version of a conjecture of Dong-Mason about lattice subalgebras of a strongly regular vertex operator algebra $V$, and give some applications. These include the existence of a canonical conformal subVOA $W\otimes G\otimes Z \subs...
We define a weak compatibility condition for the Newest Vertex Bisection algorithm on simplex grids of any dimension and show that using this condition the iterative algorithm terminates successfully. Additionally we provide an O(n) algorithm that re...
An automorphism on a graph $G$ is a bijective mapping on the vertex set $V(G)$, which preserves the relation of adjacency between any two vertices of $G$. An automorphism $g$ fixes a vertex $v$ if $g$ maps $v$ onto itself. The stabilizer of a set $S$...
An oriented graph is a directed graph without any cycle of length at most 2. To push a vertex of a directed graph is to reverse the orientation of the arcs incident to that vertex. Klostermeyer and MacGillivray defined push graphs which are equivalen...
Hunters and Rabbit game is played on a graph $G$ where the Hunter player shoots at $k$ vertices in every round while the Rabbit player occupies an unknown vertex and, if not shot, must move to a neighbouring vertex after each round. The Rabbit player...
We generalise the standard constructions of a Cayley graph in terms of a group presentation by allowing some vertices to obey different relators than others. The resulting notion of presentation allows us to represent every vertex transitive graph. A...
Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph matching m...
For an integer $t\geq 4$, a $t$-sun is a graph obtained from a $t$-vertex cycle $C$ by adding a degree-one neighbor for each vertex of $C$. Trotignon asked whether every triangle-free graph of sufficiently large chromatic number has an induced subgra...
An \emph{independent transversal} (IT) in a graph $G$ with a given vertex partition $P$ is an independent set of vertices of $G$ (i.e. it induces no edges), that consists of one vertex from each part (\emph{block}) of $P$. Over the years, various cri...
Official Repo for Google Cloud AI Platform. Find samples for Vertex AI, Google Cloud's new unified ML platform at: https://github.com/GoogleCloudPlatform/vertex-ai-samples (⭐ 479)
A new entry in the Vertex AI model catalog was spotted: model:gemini-3.1-flash-image. It looks like the rumors were true—this is the official identity of **Nano Banana 2**. While everyone was waiti...
A new entry in the Vertex AI model catalog was spotted: model:gemini-3.1-flash-image. It looks like the rumors were true—this is the official identity of **Nano Banana 2**. While everyone was waiti...
Hey all, I’m hoping someone here can point me in the right direction because I’m stuck. Last week I noticed my Google Cloud account was compromised. The attacker enabled Vertex AI (which I’ve ...
Prudent walks are self-avoiding walks on the square lattice which never step into the direction of an already occupied vertex. We study the closed version of these walks, called prudent polygons, where the last vertex is adjacent to the first one....
This paper is concerned with voting processes on graphs where each vertex holds one of two different opinions. In particular, we study the \emph{Best-of-two} and the \emph{Best-of-three}. Here at each synchronous and discrete time step, each vertex u...
We consider two variations of the discrete car parking problem where at every vertex of the integers a car arrives with rate one, now allowing for parking in two lines. a) The car parks in the first line whenever the vertex and all of its nearest n...
In this article we prove that the full automorphism group of the baby-monster vertex operator superalgebra constructed by Hoehn is isomorphic to 2xB, where B is the baby-monster sporadic finite simple group and determine irreducible modules for the...