J-Open Independent Sets in Graphs


  • Javier Hassan MSU Tawi-Tawi College of Technology and Oceanography
  • Nuruddina M. Bakar
  • Norwajir S. Dagsaan
  • Mercedita A. Langamin
  • Nurijam Hanna M. Mohammad
  • Sisteta U. Kamdon




J-Open Independent set , J-Open Independence number


Let $G\neq \overline{K}_n$ 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 $a\neq b$, $d_G(a,b)$ $\neq 1$, and $N_G(a) \backslash N_G(b) \neq \varnothing$ and $N_G(b)\backslash N_G(a) \neq \varnothing$. 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.






Nonlinear Analysis

How to Cite

J-Open Independent Sets in Graphs. (2024). European Journal of Pure and Applied Mathematics, 17(2), 922-930. https://doi.org/10.29020/nybg.ejpam.v17i2.5084

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