Domination Defect in the Edge Corona of Graphs

Abstract

Given a graph G = (V (G),E(G)), a nonempty set S \(\subseteq\) V (G) of fixed cardinality \(\gamma\)(G) - k is called a \(\zeta\)k - set of G, where 1 \(\le\) k \(\le\) \(\gamma\)(G) -1, if S gives the minimum cardinality |V (G) \ NG[S]| for all the possible subsets of V (G), each of which has \(\gamma\)(G) - k elements. This is the number of vertices in G which are left undominated by S. In this paper, the k-domination defects of graphs resulting from the binary operation edge corona G\(\diamond\)H are characterized and as a direct consequence, the corresponding k-domination defect \(\zeta\)k(G\(\diamond\)H) is then determined.