Related papers: A census of Cayley graphs

We describe computational results about undirected graphs having $10$ vertices and automorphism group isomorphic to $\mathbb{Z}/4\mathbb{Z}$.

We prove an upper bound on the number of pairwise strongly cospectral vertices in a normal Cayley graph, in terms of the multiplicities of its eigenvalues. We use this to determine an explicit bound in Cayley graphs of $\mathbb{Z}_2^d$ and…

In this paper, generalized Cayley graphs are studied. It is proved that every generalized Cayley graph of order 2p is a Cayley graph, where p is a prime. Special attention is given to generalized Cayley graphs on Abelian groups. It is…

In this work, we try to enunciate the Total chromatic number of some Cayley graphs like the Cayley graph on Symmetric group, Alternating group, Dihedral group with respect to some generating sets and some other regular graphs.

We investigate Cayley graphs of graph products by showing that graph products with vertex groups that have isomorphic Cayley graphs yield isomorphic Cayley graphs.

Given a simple undirected graph, one can construct from it a $c$-step nilpotent Lie algebra for every $c \geq 2$ and over any field $K$, in particular also over the real and complex numbers. These Lie algebras form an important class of…

We call a graph $k$-geodetic, for some $k\geq 1$, if it is connected and between any two vertices there are at most $k$ geodesics. It is shown that any hyperbolic group with a $k$-geodetic Cayley graph is virtually-free. Furthermore, in…

A graph is called a GRR if its automorphism group acts regularly on its vertex-set. Such a graph is necessarily a Cayley graph. Godsil has shown that there are only two infinite families of finite groups that do not admit GRRs : abelian…

We define the Cayley graph and its growth function for multivalued groups. We prove that if we change a finite set of generators of multivalued group, or change the starting point, we get an equivalent growth function. We prove that if we…

Suppose G is a nilpotent, finite group. We show that if {a,b} is any 2-element generating set of G, then the corresponding Cayley digraph Cay(G;a,b) has a hamiltonian path. This implies there is a hamiltonian path in every connected Cayley…

Autostackability for finitely generated groups is defined via a topological property of the associated Cayley graph which can be encoded in a finite state automaton. Autostackable groups have solvable word problem and an effective inductive…

A graph is called {\em arc-transitive} (or {\em symmetric}) if its automorphism group has a single orbit on ordered pairs of adjacent vertices, and 2-arc-transitive its automorphism group has a single orbit on ordered paths of length 2. In…

We present families of large undirected and directed Cayley graphs whose construction is related to butterfly networks. One approach yields, for every large $k$ and for values of $d$ taken from a large interval, the largest known Cayley…

A graph $X$ is $k$-spanning cyclable if for any subset $S$ of $k$ distinct vertices there is a 2-factor of $X$ consisting of $k$ cycles such that each vertex in $S$ belongs to a distinct cycle. In this paper we examine the $k$-spanning…

We study Cayley graphs of abelian groups from the perspective of quantum symmetries. We develop a general strategy for determining the quantum automorphism groups of such graphs. Applying this procedure, we find the quantum symmetries of…

A graph is called integral if all its eigenvalues are integers. A Cayley graph is called normal if its connection set is a union of conjugacy classes. We show that a non-empty integral normal Cayley graph for a group of odd order has an odd…

In this paper we are interested in the asymptotic enumeration of Cayley graphs. It has previously been shown that almost every Cayley digraph has the smallest possible automorphism group: that is, it is a digraphical regular representation…

We describe an algorithm for the exhaustive generation of non-isomorphic graphs with a given number $k \ge 0$ of hamiltonian cycles, which is especially efficient for small $k$. Our main findings, combining applications of this algorithm…

Let $k,p,q$ be three positive integers. A graph $G$ with order $n$ is said to be $k$-placeable if there are $k$ edge disjoint copies of $G$ in the complete graph on $n$ vertices. A $(p,\,q)$-graph is a graph of order $p$ with $q$ edges.…

We study those automatic sequences which are produced by an automaton whose underlying graph is the Cayley graph of a finite group. For $2$-automatic sequences, we find a characterization in terms of what we call homogeneity, and among…