690 results for Vertex · 0.096s

arxiv.org/abs/1708.09700v4

Walk entropy and walk-regularity

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)...

arxiv.org/abs/1110.0544v1

Lattice subalgebras of strongly regular vertex operator algebras

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...

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arxiv.org/abs/1507.00517v1

On The Fixed Number of Graphs

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 $S$...

arxiv.org/abs/1508.07217v1

On homomorphism of oriented graphs with respect to push operation

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...

arxiv.org/abs/2309.16533v1

Further results on the Hunters and Rabbit game through monotonicity

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...

arxiv.org/abs/2007.06432v1

Presentations for Vertex Transitive Graphs

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...

arxiv.org/abs/1705.00674v5

Vertex Nomination Via Seeded Graph Matching

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...

arxiv.org/abs/2506.10227v1

Suns in triangle-free graphs of large chromatic number

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...

arxiv.org/abs/2305.10595v1

Degree criteria and stability for independent transversals

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...

github.com/GoogleCloudPlatform/ai-platform-samples

GoogleCloudPlatform/ai-platform-samples

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)

arxiv.org/abs/0809.5232v3

Exact solution of two classes of prudent polygons

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....

arxiv.org/abs/0811.3599v2

A second row Parking Paradox

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...