J-Open Independent Sets in Graphs

Authors

  • 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

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i2.5084

Keywords:

J-Open Independent set , J-Open Independence number

Abstract

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.

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Published

2024-04-30

Issue

Section

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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