article · European Journal of Pure and Applied Mathematics · 2023

On the j-Edge Intersection Graph of Cycle Graph

Jhon Cris Bonifacio, Clarence Joy Andaya, Daryl M. Magpantay

Cited by 1Open access

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 $j=2$.

Cite this paper

APA 7

Bonifacio, J. C., Andaya, C. J., & Magpantay, D. M. (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

MLA 9

Bonifacio, Jhon Cris, et al. “On the j-Edge Intersection Graph of Cycle Graph.” European Journal of Pure and Applied Mathematics, vol. 16, no. 4, 2023, pp. 2476–98, https://doi.org/10.29020/nybg.ejpam.v16i4.4870.

Chicago

Bonifacio, Jhon Cris, Clarence Joy Andaya, and Daryl M. Magpantay. 2023. “On the j-Edge Intersection Graph of Cycle Graph.” European Journal of Pure and Applied Mathematics 16 (4): 2476–98. https://doi.org/10.29020/nybg.ejpam.v16i4.4870.

Harvard

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

BibTeX

@article{bonifacio2023edge,
  title = {{On the j-Edge Intersection Graph of Cycle Graph}},
  author = {Bonifacio, Jhon Cris and Andaya, Clarence Joy and Magpantay, Daryl M.},
  journal = {European Journal of Pure and Applied Mathematics},
  volume = {16},
  number = {4},
  pages = {2476--2498},
  year = {2023},
  doi = {10.29020/nybg.ejpam.v16i4.4870}
}

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