Inverse degree, randić index and harmonic index of graphs

Kinkar Ch Das; Selvaraj Balachandran; Ivan Gutman

doi:10.2298/AADM1702304D

Inverse degree, randić index and harmonic index of graphs

Kinkar Ch Das
, Selvaraj Balachandran
, Ivan Gutman

Department of Mathematics

SASTRA
University of Kragujevac

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

22 Scopus citations

Abstract

Let G be a graph with vertex set V and edge set E. Let di be the degree of the vertex v_i of G. The inverse degree, Randić index, and harmonic index of G are defined as ID =Σ_vi∈V 1/d_i, R =Σ_vivj∈E 1/√d_i d_j, and H = Σ_vivj∈E 2/(d_i + d_j ), respectively. We obtain relations between ID and R as well as between ID and H. Moreover, we prove that in the case of trees, ID > R and ID > H.

Original language	English
Pages (from-to)	304-313
Number of pages	10
Journal	Applicable Analysis and Discrete Mathematics
Volume	11
Issue number	2
DOIs	https://doi.org/10.2298/AADM1702304D
State	Published - 2017

Keywords

Degree (of vertex)
Harmonic index
Inverse degree
Randić index

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title = "Inverse degree, randi{\'c} index and harmonic index of graphs",

abstract = "Let G be a graph with vertex set V and edge set E. Let di be the degree of the vertex vi of G. The inverse degree, Randi{\'c} index, and harmonic index of G are defined as ID =Σvi∈V 1/di, R =Σvivj∈E 1/√di dj, and H = Σvivj∈E 2/(di + dj ), respectively. We obtain relations between ID and R as well as between ID and H. Moreover, we prove that in the case of trees, ID > R and ID > H.",

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author = "Das, \{Kinkar Ch\} and Selvaraj Balachandran and Ivan Gutman",

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T1 - Inverse degree, randić index and harmonic index of graphs

AU - Das, Kinkar Ch

AU - Balachandran, Selvaraj

AU - Gutman, Ivan

PY - 2017

Y1 - 2017

N2 - Let G be a graph with vertex set V and edge set E. Let di be the degree of the vertex vi of G. The inverse degree, Randić index, and harmonic index of G are defined as ID =Σvi∈V 1/di, R =Σvivj∈E 1/√di dj, and H = Σvivj∈E 2/(di + dj ), respectively. We obtain relations between ID and R as well as between ID and H. Moreover, we prove that in the case of trees, ID > R and ID > H.

AB - Let G be a graph with vertex set V and edge set E. Let di be the degree of the vertex vi of G. The inverse degree, Randić index, and harmonic index of G are defined as ID =Σvi∈V 1/di, R =Σvivj∈E 1/√di dj, and H = Σvivj∈E 2/(di + dj ), respectively. We obtain relations between ID and R as well as between ID and H. Moreover, we prove that in the case of trees, ID > R and ID > H.

KW - Degree (of vertex)

KW - Harmonic index

KW - Inverse degree

KW - Randić index

UR - https://www.scopus.com/pages/publications/85031934645

U2 - 10.2298/AADM1702304D

DO - 10.2298/AADM1702304D

M3 - Article

AN - SCOPUS:85031934645

SN - 1452-8630

VL - 11

SP - 304

EP - 313

JO - Applicable Analysis and Discrete Mathematics

JF - Applicable Analysis and Discrete Mathematics

IS - 2

ER -

Inverse degree, randić index and harmonic index of graphs

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