Line Graph Associated to Graph of a Near-Ring with Respect to an Ideal

Authors

  • Moytri Sarmah Department of Mathematicas, Girijananda Chowdhury Institute of Manage- ment and Technology, Guwahati-781017, India https://orcid.org/0000-0003-1259-3766
  • Kuntala Patra Department of Mathematics, Gauhati University, Guwahati-781014, India

DOI:

https://doi.org/10.5556/j.tkjm.52.2021.3326

Keywords:

Graph, Line graph, Near-ring, Ideal

Abstract

Let $N$ be a near-ring and $I$ be an ideal of $N$. The graph of $N$ with respect to $I$ is a graph with $V (N )$ as vertex set and any two distinct vertices $x$ and $y$ are adjacent if and only if $xNy \subseteq I$ or $yNx \subseteq I$. This graph is denoted by $G_I(N)$. We define the line graph of $G_I(N)$ as a graph with each edge of $G_I (N )$ as vertex and any two distinct vertices are adjacent if and only if their corresponding edges share a common vertex in the graph $G_I (N )$. We denote this graph by $L(G_I (N ))$. We have discussed the diameter, girth, clique number, dominating set of $L(G_I(N))$. We have also found conditions for the graph $L(G_I(N))$ to be acycle graph.

References

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S. Bhavanari, S. P. Kuncham and B. S. Kedukodi, Graph of a near ring with respect to an ideal, Communication in Algebra, 38, (2010), 1957 - 1967.

W. B. Vasantha Kandasamy, Smarandache near-rings, American Reasearch Press, Rehoboth, 2002.

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Published

2021-08-01

How to Cite

Sarmah, M. ., & Patra, K. (2021). Line Graph Associated to Graph of a Near-Ring with Respect to an Ideal. Tamkang Journal of Mathematics, 52(3), 341-347. https://doi.org/10.5556/j.tkjm.52.2021.3326

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Papers