Edge colorability of unitary endo-cayley graphs of cyclic groups

Abstract

Let n be a positive integer greater than 1, ℤ_n the ring of integer modulo n, f an endomorphism on ℤ_n and U_n the set of all units in ℤ_n. The unitary endo-Cayley digraph, denoted by endo-Cay_f (ℤ_n, U_n), is the digraph whose vertex set is ℤ_n and a vertex u is adjacent to v if v = f(u) + u ∈ U_n for some u ∈ U_n. We study about the edge coloring properties of undirected unitary endo-Cayley graphs, endo-Cay_f (ℤ_n, U_n). Their edge chromatic number are disclosed. We also determine what class they are of. Moreover, some basic properties involving edge coloring are investigated.