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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
- 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