On inverse degree and topological indices of graphs

Kinkar Ch Das; Kexiang Xu; Jinlan Wang

doi:10.2298/FIL1608111D

On inverse degree and topological indices of graphs

Kinkar Ch Das
, Kexiang Xu
, Jinlan Wang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

Let G = (V; E) be a simple graph of order n and size m with maximum degree Δ and minimum degree δ. The inverse degree of a graph G with no isolated vertices is defined as (Formula presented)where d_i is the degree of the vertex v_i ∈ V(G). In this paper, we obtain several lower and upper bounds on ID(G) of graph G and characterize graphs for which these bounds are best possible. Moreover, we compare inverse degree ID(G) with topological indices (GA₁-index, ABC-index, Kf -index) of graphs.

Original language	English
Pages (from-to)	2111-2120
Number of pages	10
Journal	Filomat
Volume	30
Issue number	8
DOIs	https://doi.org/10.2298/FIL1608111D
State	Published - 2016

Keywords

ABC-index
GA-index
Inverse degree
Kf -index
Simple graph
Vertex degree

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10.2298/FIL1608111D

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N2 - Let G = (V; E) be a simple graph of order n and size m with maximum degree Δ and minimum degree δ. The inverse degree of a graph G with no isolated vertices is defined as (Formula presented)where di is the degree of the vertex vi ∈ V(G). In this paper, we obtain several lower and upper bounds on ID(G) of graph G and characterize graphs for which these bounds are best possible. Moreover, we compare inverse degree ID(G) with topological indices (GA1-index, ABC-index, Kf -index) of graphs.

AB - Let G = (V; E) be a simple graph of order n and size m with maximum degree Δ and minimum degree δ. The inverse degree of a graph G with no isolated vertices is defined as (Formula presented)where di is the degree of the vertex vi ∈ V(G). In this paper, we obtain several lower and upper bounds on ID(G) of graph G and characterize graphs for which these bounds are best possible. Moreover, we compare inverse degree ID(G) with topological indices (GA1-index, ABC-index, Kf -index) of graphs.

KW - ABC-index

KW - GA-index

KW - Inverse degree

KW - Kf -index

KW - Simple graph

KW - Vertex degree

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JO - Filomat

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ER -

On inverse degree and topological indices of graphs

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Keywords

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