Zobrazeno 1 - 10
of 202
pro vyhledávání: '"Primary: 05C25"'
Autor:
Podestá, Ricardo A., Videla, Denis E.
In this work we consider the class of Cayley graphs known as generalized Paley graphs (GP-graphs for short) given by $\Gamma(k,q) = Cay(\mathbb{F}_q, \{x^k : x\in \mathbb{F}_q^* \})$, where $\mathbb{F}_q$ is a finite field with $q$ elements, both in
Externí odkaz:
http://arxiv.org/abs/2410.00281
We examine bicoset digraphs and their natural properties from the point of view of symmetry. We then consider connected bicoset digraphs that are $X$-joins with collections of empty graphs, and show that their automorphism groups can be obtained from
Externí odkaz:
http://arxiv.org/abs/2409.11092
For a finite group $G$, the vertices of the prime graph $\Gamma(G)$ are the primes that divide $|G|$, and two vertices $p$ and $q$ are connected by an edge if and only if there is an element of order $pq$ in $G$. Prime graphs of solvable groups as we
Externí odkaz:
http://arxiv.org/abs/2407.06595
Autor:
Barber, Rachel, Dobson, Ted
It has long been known that a vertex-transitive graph $\Gamma$ is isomorphic to a double coset graph $\text{Cos}(G,H,S)$ of a transitive group $G\le\text{Aut}(\Gamma)$, a vertex stabilizer $H\le G$, and some subset $S\subseteq G$. We show that the au
Externí odkaz:
http://arxiv.org/abs/2407.02316
In this note, we extend results about unique $n^{\textrm{th}}$ roots and cancellation of finite disconnected graphs with respect to the Cartesian, the strong and the direct product, to the rooted hierarchical products, and to a modified lexicographic
Externí odkaz:
http://arxiv.org/abs/2407.02615
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
The degree-diameter problem for graphs is to find the largest number of vertices a graph can have given its diameter and maximum degree. We show we can realize this problem in terms of quasigroups, 1-factors and permutation groups. Our investigation
Externí odkaz:
http://arxiv.org/abs/2405.12374
Autor:
Árnadóttir, Arnbjörg Soffía, de Bruyn, Josse van Dobben, Kar, Prem Nigam, Roberson, David E., Zeman, Peter
Sabidussi's theorem [Duke Math. J. 28, 1961] gives necessary and sufficient conditions under which the automorphism group of a lexicographic product of two graphs is a wreath product of the respective automorphism groups. We prove a quantum version o
Externí odkaz:
http://arxiv.org/abs/2402.12344
Autor:
Carleton, Rachel, Lewis, Mark
Let $G$ be a finite group. Recall that an $A$-group is a group whose Sylow subgroups are all abelian. In this paper, we investigate the upper bound on the diameter of the commuting graph of a solvable $A$-group. Assuming that the commuting graph is c
Externí odkaz:
http://arxiv.org/abs/2402.10927
Autor:
Lesnevich, Nathan R. T.
A spline is an assignment of polynomials to the vertices of a graph whose edges are labeled by ideals, where the difference of two polynomials labeling adjacent vertices must belong to the corresponding ideal. The set of splines forms a ring. We cons
Externí odkaz:
http://arxiv.org/abs/2401.14380