@article{J-Open Independent Sets in Graphs_2024, place={Maryland, USA}, volume={17}, url={https://www.ejpam.com/index.php/ejpam/article/view/5084}, DOI={10.29020/nybg.ejpam.v17i2.5084}, abstractNote={Let $G
eq \overline{K}_n$ be a graph with vertex and edge-sets $V(G)$ and $E(G)$, respectively. Then\linebreak $O$ $\subseteq$ $V(G)$ is called a J-open independent set of $G$ if for every $a,b \in V(G)$ where $a
eq b$, $d_G(a,b)$ $
eq 1$, and $N_G(a) \backslash N_G(b)
eq \varnothing$ and $N_G(b)\backslash N_G(a)
eq \varnothing$. The maximum cardinality of a J-open independent set of G, denoted by $\alpha_J(G)$, 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.}, number={2}, journal={European Journal of Pure and Applied Mathematics}, year={2024}, month={Apr.}, pages={922–930} }