(untitled) (European Journal of Pure and Applied Mathematics, 2024)
Let G be a connected graph and uv ∈ E(G). We say, the vertex v even sum dominates u (u even sum dominates v) if deg(v)+deg(u) is an even number. A set S is an even sum dominating set (ESDS) if every vertex v ∈ V is either in S or even sum dominated by a vertex in S. An even sum dominating set S is a mimimal even sum dominating set if no proper subset S′⊂ S is an even sum dominating set. The even sum domination number γes(G) of a graph G is the minimum cardinality of an even sum dominating set of G. In this paper, we discuss some properties and bounds for this concept. We also derive even sum domination number for some standard graphs.