Annihilator domination number of tensor product of path graphs

Abstract

An annihilator dominating set (ADS) is a representative technique for finding the induced subgraph of a graph which can help to isolate the vertices. A dominating set of graph G is called ADS if its induced subgraph is containing only isolated vertices. The annihilator domination number of G, denoted by ?a(G) is the minimum cardinality of ADS. The tensor product of graphs G and H signified by G × H is a graph with vertex set V = V (G)×V (H) and edge {(u, v),(u 0 , v0 )} ? E whenever (u, u0 ) ? E(G) and (v, v0 ) ? E(H). In this paper, we deduce exact values of annihilator domination number of tensor product of Pm and Pn, m, n ? 2. Further, we investigated some lower and upper bounds for annihilator domination number of tensor product of path graphs.