(untitled) (European Journal of Pure and Applied Mathematics, 2023)
A subset T={v_1, v_2, …, v_m} of vertices of an undirected graph G is called a J^2-set if N_G^2[v_i]N_G^2[v_j] eq for every i eq j, where i,j{1, 2, …, m}. A J^2-set is called a J^2-hop dominating in G if for every aV(G)T, there exists bT such that d_G(a,b)=2. The J^2-hop domination number of G, denoted by γ_J^2h(G), is the maximum cardinality among all J^2-hop dominating sets in G. In this paper, we introduce this new parameter and we determine its connections with other known parameters in graph theory. We derive its bounds with respect to the order of a graph and other known parameters on a generalized graph, join and corona of two graphs. Moreover, we obtain exact values of the parameter for some special graphs and shadow graphs using the characterization results that are formulated in this study.