(untitled) (European Journal of Pure and Applied Mathematics, 2024)
Let G eq K_n be a graph with vertex and edge-sets V(G) and E(G), respectively. ThenO V(G) is called a J-open independent set of G if for every a,b V(G) where a eq b, d_G(a,b) eq 1, and N_G(a) N_G(b) eq and N_G(b)N_G(a) eq . The maximum cardinality of a J-open independent set of G, denoted by α_J(G), is called the J-open independence number of G. In this paper, we introduce new independence parameter called J-open independence. We show that this parameter is always less than or equal to the standard independence (resp. J-total domination) parameter of a graph. In fact, their differences can be made arbitrarily large. In addition, we show that J-open independence parameter is incomparable with hop independence parameter. Moreover, we derive some formulas and bounds of the parameter for some classes of graphs and the join of two graphs.