On a generalized Cayley graph of column matrices of elements of a finite group

Abstract

We introduce a new generalization of Cayley graphs. Moreover, we establish some basic properties of this new type of graph and we determine its structure under some assumptions.

The Structure of the Generalized Cayley Graph Cay_m (〖 D〗_2n,S) of Valency Three

“…He denoted it by Caym(G,S) for every m ≥ 1, and it is clear that if m = 1 then we will achieve the known Cayley graph Cay(G,S). In 2021, Neamah , Erfanian and others [4,5] established the structure of a generalized Cayley graph Caym(G,S), when Cay(G,S) is a cycle graph C n , for all n ≥ 3.…”

“…al. in [5], for all n ≥ 3 and m ≥ 2. Moreover, , the structure of the Cay m (G, S) when Cay(G, S) is a cycle graph C n by [8].…”