The Intersection Graph of Subgroups of the Dihedral Group of Order 2pq

Peshawa M.  Khudhur; Rashad R.  Haji; Sanhan M.S.  Khasraw

doi:10.24996/ijs.2021.62.12.30

Authors

Peshawa M. Khudhur Department of Mathematics, Faculty of Science, Soran University, Erbil, Kurdistan Region, Iraq https://orcid.org/0000-0003-0062-7519
Rashad R. Haji Department of Mathematics, College of Education, Salahaddin University-Erbil, Erbil, Kurdistan Region, Iraq
Sanhan M.S. Khasraw Department of Mathematics, College of Basic Education, Salahaddin University-Erbil, Erbil, Kurdistan Region, Iraq

DOI:

https://doi.org/10.24996/ijs.2021.62.12.30

Keywords:

dihedral group, intersection graph of subgroups, detour distance, mean distance

Abstract

For a finite group G, the intersection graph of G is the graph whose vertex set is the set of all proper non-trivial subgroups of G, where two distinct vertices are adjacent if their intersection is a non-trivial subgroup of G. In this article, we investigate the detour index, eccentric connectivity, and total eccentricity polynomials of the intersection graph of subgroups of the dihedral group for distinct primes . We also find the mean distance of the graph .