Related papers: Algebraic Cayley Graphs over Finite Fields
We improve upper bounds of F. R. K. Chung and of M. Lu, D. Wan, L.-P. Wang, X.-D. Zhang on the diameter of some Cayley graphs constructed from polynomials over finite fields.
We present simple graph-theoretic characterizations of Cayley graphs for left-cancellative monoids, groups, left-quasigroups and quasigroups. We show that these characterizations are effective for the end-regular graphs of finite degree.
Due to their elegant and simple nature, unitary Cayley graphs have been an active research topic in the literature. These graphs are naturally connected to several branches of mathematics, including number theory, finite algebra,…
In this paper, rough approximations of Cayley graphs are studied and rough edge Cayley graphs are introduced. Furthermore, a new algebraic definition called pseudo-Cayley graphs containing Cayley graphs is proposed. Rough approximation is…
The results of computer searches for large graphs with given (small) degree and diameter are presented. The new graphs are Cayley graphs of semidirect products of cyclic groups and related groups. One fundamental use of our ``dense graphs''…
We give a construction of strongly regular Cayley graphs on finite fields $\F_q$ by using union of cyclotomic classes and index 4 Gauss sums. In particular, we obtain two infinite families of strongly regular graphs with new parameters.
Infinite analogues of the Paley graphs are constructed, based on uncountably many infinite but locally finite fields. Weil's estimate for character sums shows that they are all isomorphic to the random or universal graph of Erd\H os,…
In this paper, we give a construction of strongly regular Cayley graphs on the additive groups of finite fields based on three-valued Gauss periods. As consequences, we obtain two infinite families and one sporadic example of new strongly…
In this paper, we study new Cayley graphs over the additive group of Galois rings. First we prove that they are expander graphs by using a Weil-Carlitz-Uchiyama type estimation of character sums for Galois rings. We also show that Cayley…
In this paper, we will study the chromatic number of Cayley graphs of algebraic groups that arise from algebraic constructions. Using Lang-Weil bound and representation theory of finite simple groups of Lie type, we will establish lower…
We construct a sequence of finite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. A similar construction is used to give graph sequences that…
Perfect code in Cayley graphs and Cayley sum graphs is studied extensively in recent years. In this paper, we consider perfect code in generalized Cayley graphs.
Researchers in the past have studied eigenvalues of Cayley digraphs or graphs. We are interested in characterizing Cayley digraphs on a finite Abelian group G whose eigenvalues are algebraic integers in a given number field K. And we…
We construct a 2-generated group $\Gamma $ such that its Cayley graph possesses finite connected subsets with arbitrarily big finite Heesch number.
We consider the case in which mixed graphs (with both directed and undirected edges) are Cayley graphs of Abelian groups. In this case, some Moore bounds were derived for the maximum number of vertices that such graphs can attain. We first…
In this paper, we introduce the concept of $k$-integral graphs. A graph $\Gamma$ is called $k$-integral if the extension degree of the splitting field of the characteristic polynomial of $\Gamma$ over rational field $\mathbb Q$ is equal to…
The degree-diameter problem seeks to find the largest possible number of vertices in a graph having given diameter and given maximum degree. Very often the problem is studied for restricted families of graph such as vertex-transitive or…
A few properties of unitary Cayley graphs are explored using their eigenvalues. It is shown that the adjacency algebra of a unitary Cayley graph is a coherent algebra. Finally, a class of unitary Cayley graphs that are distance regular are…
A connected undirected graph is called \emph{geodetic} if for every pair of vertices there is a unique shortest path connecting them. It has been conjectured that for finite groups, the only geodetic Cayley graphs are odd cycles and…
We present simple graph-theoretic characterizations of Cayley graphs for monoids, semigroups and groups. We extend these characterizations to commutative monoids, semilattices, and abelian groups.