# Eccentric distance sum and adjacent eccentric distance sum index of complement of subgroup graphs of dihedral group

Abdussakir, Abdussakir, Susanti, Elly, Hidayati, Nurul and Ulya, Nanda M. (2019) Eccentric distance sum and adjacent eccentric distance sum index of complement of subgroup graphs of dihedral group. Presented at Annual Conference of Science and Technology, 30 Aug 2018, Malang, Indonesia.

## Abstract

Let G = (V(G),E(G)) is a connected simple graph. Let ec(v) is the eccentricity of vertex v, D(v) = Σu∈V(G) d(u,v) is the sum of all distances from vertex v and deg(v) is the degree of vertex v in G. The eccentric distance sum index of G is defined as ξd(G) = Σv∈V(G)ec(v)D(v) and the adjacent eccentric distance sum index of G is defined as ${\xi }^{sv}(G)=\displaystyle {\sum }_{v\in V(G)}\frac{ec(v)D(v)}{\deg (v)}$. For positive integer m and m ≥ 3, let D2m be dihedral group of order 2m and N is a normal subgroup of D2m. The subgroup graph ΓN(D2m) of dihedral group D2m is a simple graph with vertex set D2m and two distinct vertices x and y are adjacent if and only if xy ∈ N. In the present paper, we compute eccentric distance sum and adjacent eccentric distance sum index of complement of subgroup graph of dihedral group D2m. Total eccentricity, eccentric connectivity index, first Zagreb index, and second Zagreb index of these graphs are also determined.

Item Type: Conference (Paper) eccentric distance sum; adjacent eccentric distance sum; subgroup graphs; dihedral group 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010105 Group Theory and Generalisations Faculty of Mathematics and Sciences > Department of Mathematics Abdussakir Abdussakir 17 Dec 2019 10:32