(untitled) (European Journal of Pure and Applied Mathematics, 2025)
A set S V(G) is a hop independent set in an undirected graph G if d_G(v,w) e 2 for any two distinct vertices v, w S. The maximum cardinality among the hop independent sets in G, denoted by α_h(G), is called the hop independence number of G. The hop independent sets in the shadow graph, complementary prism, edge corona and disjunctive products of two graphs are characterized. These characterizations are used to determine the exact or sharp bounds of the hop independence numbers of these graphs. Furthermore, we show that the hop independent set decision problem (HISP) is NP-complete.