On Intersection Graph of Dihedral Group

Abstract

Let G be a finite group. The intersection graph of G is a graph whose vertex set is the set of all proper non-trivial subgroups of G and two distinct vertices H and K are adjacent if and only if H K ≠ \e\, where e is the identity of the group G. In this paper, we investigate some properties and exploring some topological indices such as Wiener, Hyper-Wiener, first and second Zagreb, Schultz, Gutman and eccentric connectivity indices of the intersection graph of D2n for n=p2, p is prime. We also find the metric dimension and the resolving polynomial of the intersection graph of D2p2.