Identity Intersection graph of a group

A. Sivagami; J. Vijaya Xavier Parthiban

Identity Intersection graph of a group

Authors

A. Sivagami Research Scholar, Reg No.20121272092007, Department of Mathematics, St. John’s College, Palayamkottai, Tamilnadu, India Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627012, Tamilnadu, India
J. Vijaya Xavier Parthiban Department of Mathematics, St. John’s College, Palayamkottai, Tamilnadu, India

Keywords:

Identity Intersection graph, Star graph, finite group, p-Sylow subgroup.

Abstract

Let G be a group with identity e. The Identity Intersection graph Γ_II(G) of G is a graph with V(Γ_II(G))=G and two distinct vertices x and y are adjacent in Γ_II(G) if and only if < x >∩ < y >= {e}, where < x >is the cyclic subgroup of G generated by x∈G. In this paper, we want to explore how the group theoretical properties of G can effect on the graph theoretical properties of Γ_II(G). Some characterizations for fundamental properties of Γ_II(G) have also been obtained.

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Published

2024-09-09

How to Cite

A. Sivagami, & J. Vijaya Xavier Parthiban. (2024). Identity Intersection graph of a group. Journal of Computational Analysis and Applications (JoCAAA), 33(08), 519–521. Retrieved from https://eudoxuspress.com/index.php/pub/article/view/1364