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

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

Authors :
Abdussakir Abdussakir
Elly Susanti
Nanda M. Ulya
Nurul Hidayati
Source :
Journal of Physics: Conference Series. 1375:012065
Publication Year :
2019
Publisher :
IOP Publishing, 2019.

Abstract

Let G = (V(G),E(G)) is a connected simple graph. Let ec(v) is the eccentricity of vertex v, D(v) = Σ u∈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) = Σ v∈V(G) ec(v)D(v) and the adjacent eccentric distance sum index of G is defined as ξ s v ( G ) = ∑ v ∈ V ( G ) e c ( v ) D ( v ) deg ( v ) . For positive integer m and m ≥ 3, let D 2m be dihedral group of order 2m and N is a normal subgroup of D 2m . The subgroup graph Γ N (D 2m ) of dihedral group D 2m is a simple graph with vertex set D 2m 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 D 2m . Total eccentricity, eccentric connectivity index, first Zagreb index, and second Zagreb index of these graphs are also determined.

Details

ISSN :
17426596 and 17426588
Volume :
1375
Database :
OpenAIRE
Journal :
Journal of Physics: Conference Series
Accession number :
edsair.doi...........4851cc90472454bb28f243237e0a51b9
Full Text :
https://doi.org/10.1088/1742-6596/1375/1/012065