On the j-Edge Intersection Graph of Cycle Graph

Authors

  • Jhon Cris Bonifacio
  • Clarence Joy Andaya
  • Daryl Magpantay BATANGAS STATE UNIVERSITY

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i4.4870

Keywords:

New Graph

Abstract

This paper defines a new class of graphs using the spanning subgraphs of a cycle graph as vertices. This class of graphs is called $j$-edge intersection graph of cycle graph, denoted by $E_{C_{(n,j)}}$. The vertex set of $E_{C_{(n,j)}}$ is the set of spanning subgraphs of cycle graph with $j$ edges where $n \geq 3$ and $j$ is a nonnegative integer such that $1 \leq j \leq n$. Moreover, two distinct vertices are adjacent if they have exactly one edge in common. $E_{C_{(n,j)}}$ is considered as a simple graph. Furthermore, $E_{C_{(n,j)}}$ is characterized by the value of $j$ that is when $j=1$ or $\lceil \frac{n}{2} \rceil < j \leq n$ and $2 \leq j \leq \lceil \frac{n}{2} \rceil$. When $j=1$ or $\lceil \frac{n}{2} \rceil < j \leq n$, the new graph only produced an empty graph. Hence, the proponents only considered the value when $2 \leq j \leq \lceil \frac{n}{2} \rceil$ in determining the order and size of $E_{C_{(n,j)}}$. Moreover, this paper discusses necessary and sufficient conditions where the $j$-edge intersection graph of $C_n$ is isomorphic to the cycle graph. Furthermore, the researchers determined a lower bound for the independence number, and an upper bound for the domination number of $E_{C_{(n,j)}}$ when $j=2$.

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Published

2023-10-30

How to Cite

Bonifacio, J. C., Andaya, C. J., & Magpantay , D. (2023). On the j-Edge Intersection Graph of Cycle Graph. European Journal of Pure and Applied Mathematics, 16(4), 2476–2498. https://doi.org/10.29020/nybg.ejpam.v16i4.4870

Issue

Section

Nonlinear Analysis

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