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of 77
pro vyhledávání: '"05C25, 05C69"'
Let $G$ be a finite simple graph, and $J_G$ denote the binomial edge ideal of $G$. In this article, we first compute the $\mathrm{v}$-number of binomial edge ideals corresponding to Cohen-Macaulay closed graphs. As a consequence, we obtain the $\math
Externí odkaz:
http://arxiv.org/abs/2405.15354
Autor:
Rahimi, Shahin, Nikseresht, Ashkan
Let $R$ be a finite ring with identity. The unit graph (unitary Cayley graph) of $R$ is the graph with vertex set $R$, where two distinct vertices $x$ and $y$ are adjacent exactly whenever $x+y$ is a unit in $R$ ($x-y$ is a unit in $R$). Here, we stu
Externí odkaz:
http://arxiv.org/abs/2404.07189
A perfect code in a graph is an independent set of the graph such that every vertex outside the set is adjacent to exactly one vertex in the set. A circulant graph is a Cayley graph of a cyclic group. In this paper we study perfect codes in circulant
Externí odkaz:
http://arxiv.org/abs/2403.02205
Autor:
Rahimi, Shahin, Nikseresht, Ashkan
Publikováno v:
Finite fields and their applications, Vol. 96 (2024), article no. 102428
Suppose that $F$ is a finite field and $R=M_n(F)$ is the ring of $n$-square matrices over $F$. Here we characterize when the Cayley graph of the additive group of $R$ with respect to the set of invertible elements of $R$, called the unitary Cayley gr
Externí odkaz:
http://arxiv.org/abs/2311.15255
Publikováno v:
Journal of Algebraic Combinatorics 59 (2024) 735--759
Let $\Ga = (V, E)$ be a graph and $a, b$ nonnegative integers. An $(a, b)$-regular set in $\Ga$ is a nonempty proper subset $D$ of $V$ such that every vertex in $D$ has exactly $a$ neighbours in $D$ and every vertex in $V \setminus D$ has exactly $b$
Externí odkaz:
http://arxiv.org/abs/2310.01793
In this paper, we introduce a new graph structure, called the $direct~ sum ~graph$ on a finite dimensional vector space. We investigate the connectivity, diameter and the completeness of $\Gamma_{U\oplus W}(\mathbb{V})$. Further, we find its dominati
Externí odkaz:
http://arxiv.org/abs/2310.00251
Autor:
Cockburn, Sally, Klivans, Max
Praeger-Xu graphs are connected, symmetric, 4-regular graphs that are unusual both in that their automorphism groups are large, and in that vertex stabilizer subgroups are also large. Determining number and distinguishing number are parameters that m
Externí odkaz:
http://arxiv.org/abs/2309.11474
A set $D$ of vertices is a strong dominating set in a graph $G$, if for every vertex $x\in V(G) \setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $deg(x) \leq deg(y)$. The strong domination number $\gamma_{st}(G)$ of $G$ is the minimum ca
Externí odkaz:
http://arxiv.org/abs/2306.01608
Autor:
Zhang, Jun-Yang
A perfect code $C$ in a graph $\Gamma$ is an independent set of vertices of $\Gamma$ such that every vertex outside of $C$ is adjacent to a unique vertex in $C$, and a total perfect code $C$ in $\Gamma$ is a set of vertices of $\Gamma$ such that ever
Externí odkaz:
http://arxiv.org/abs/2210.03336
Autor:
Yip, Chi Hoi
Publikováno v:
Algebr. Comb. 6 (2023), no. 4, 901-905
We show the maximality of subfields as cliques in a special family of Cayley graphs defined on the additive group of a finite field. In particular, this confirms a conjecture of Yip on generalized Paley graphs.
Comment: exposition improved, 5 pa
Comment: exposition improved, 5 pa
Externí odkaz:
http://arxiv.org/abs/2209.00864