For a nonabelian group G, the non-commuting graph Γ G of G is defined as the graph with vertexset G−Z(G), where Z(G) is the center of G, and two distinct vertices of Γ G are adjacent if they do not commute in G. In this paper, we investigate the detour index, eccentric connectivity and total eccentricity polynomials of the non-commuting graph on D 2n . We also find the mean distance of the non-commuting graph on D 2n .

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  .

The aim of this paper is to use some concepts of nonstandard analysis given by Robinson, A. and axiomataized by Nelson, E. to prove some theorems concerning the approximation of integrals and the convergence of sequences and series.

For a nonabelian group G, the non-commuting graph Γ G of G is defined as the graph with vertex set G − Z(G), where Z(G) is the center of G, and two distinct vertices of Γ G are adjacent if they do not commute in G. In this paper, we investigate the detour index, eccentric connectivity and total eccentricity polynomials of non-commuting graph on D 2n . We also find the mean distance of non-commuting graph on D 2n .