(untitled) (European Journal of Pure and Applied Mathematics, 2023)
Let G be a connected graph. A set S of vertices in G is a 1-movable 2-resolving hop dominating set of G if S is a 2-resolving hop dominating set in G and for every v S, either S{v} is a 2-resolving hop dominating set of G or there exists a vertex u ((V (G) S) N_G(v)) such that (S {v}) {u} is a 2-resolving hop dominating set of G. The 1-movable 2-resolving hop domination number of G, denoted by γ^1_m2Rh(G) is the smallest cardinality of a 1-movable 2-resolving hop dominating set of G. In this paper, we investigate the concept and study it for graphs resulting from some binary operations. Specifically, we characterize the 1-movable 2-resolving hop dominating sets in the join, corona and lexicographic products of graphs, and determine the bounds of the 1-movable 2-resolving hop domination number of each of these graphs.