On the k-restricted Intersection Graph

Authors

  • Mariane Eliz Pelagio Batangas State University, The National Engineering University
  • Kathlen Mendoza Batangas State University, The National Engineering University
  • Neil Mame Batangas State University, The National Engineering University

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i3.5240

Keywords:

New Graph, Intersection Graph

Abstract

The problem on intersection graph was introduced by Szpilrajn-Marczewski in 1945. This study introduces a new variant of intersection graph, called the k-restricted intersection graph. Let Sn be a nonempty n-element set, for some positive integer n and let S(n,k) be the set of all the k-element subsets of Sn where 0kn. A k-restricted intersection graph, denoted by GS(n,k), is a graph with vertex set  S(n,k) such that two vertices A,BS(n,k) are adjacent whenever AB and AB. Here, we determined the order and size of GS(n,k). Moreover, some parameters such as independence number, domination number, and isolate domination number of the k-restricted intersection graph were established. Finally, necessary and sufficient conditions for a GS(n,k) to be isomorphic to the cycle graph and complete graph were determined.

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Published

2024-07-31

Issue

Section

Nonlinear Analysis

How to Cite

On the k-restricted Intersection Graph. (2024). European Journal of Pure and Applied Mathematics, 17(3), 1779-1803. https://doi.org/10.29020/nybg.ejpam.v17i3.5240