Line graph associated to the intersection graph of ideals of rings
Abstract
Let R be a ring with unity and I(R)∗ are all non-trivial left ideals of R. The intersection graph of ideals of R is denoted by G(R) is an undirected simple graph with vertex set I(R)∗ and two distinct vertices I and J are adjacent if and only if I∩J ≠ 0. In this article, we investigate some basic properties of the line graph associated to G(R), denoted by L(G(R)). Moreover, we investigate completeness, unicyclicness, bipartiteness, planarity, outerplanarity, ring graph, diameter, girth and clique of L(G(Zn)). We also investigate some basic properties of L(G(R)) for left Artinian ring and finally, we determine the domination number and bondage number of L(G(Zn)).
Copyright © 2021 Laithun Boro, Madan Mohan Singh, Jituparna Goswami. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
L. Boro, M. M. Singh, J. Goswami, Line graph associated to the intersection graph of ideals of rings, J. Math. Comput. Sci. 11 (2021), 2736–2745. https://doi.org/10.28919/jmcs/5567
BibTeX
@article{Boro2021,
author = {Boro, Laithun and Singh, Madan Mohan and Goswami, Jituparna},
title = {Line graph associated to the intersection graph of ideals of rings},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {2736--2745},
doi = {10.28919/jmcs/5567}
}