Abstract
In this paper, the group homomorphism graph is introduced and investigated. The group homomorphism graph, denoted by [Formula: see text], is an undirected graph in which the vertex set contains all homomorphisms excluding the monomorphisms and the zero homomorphism from the group [Formula: see text] to the group [Formula: see text], and two distinct vertices are adjacent if and only if the intersection of their kernels is non-trivial. We investigate the interplay between the graph-theoretic properties of this graph with algebraic properties of the groups. In this work, connectedness, diameter, clique number, chromatic number, domination number, independence number, etc. are found.
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