A short note on Hyper Zagreb Index

Suresh Elumalai; Toufik Mansour; Mohammad Ali Rostami; G. B.A. Xavier

doi:https://doi.org/10.5269/bspm.v37i2.29148

A short note on Hyper Zagreb Index

Suresh Elumalai, Toufik Mansour, Mohammad Ali Rostami, G. B.A. Xavier

Department of Mathematics

University of Haifa

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

Abstract

In this paper, we present and analyze the upper and lower bounds on the Hyper-Zagreb index χ²(G) of graph G in terms of the number of vertices (n), number of edges (m), maximum degree (∆), minimum degree (δ) and the inverse degree (ID(G)). In addition, a counter example on the upper bound of the second Zagreb index for Theorems 2.2 and 2.4 from_ [20] is provided. Finally, we present the lower and upper bounds on χ²(G) + χ²(G), where G denotes the complement of G.

Original language	American English
Pages (from-to)	51-58
Number of pages	8
Journal	Boletim da Sociedade Paranaense de Matematica
Volume	37
Issue number	2
DOIs	https://doi.org/10.5269/bspm.v37i2.29148
State	Published - 2019

Keywords

First Zagreb index
Hyper Zagreb index
Second Zagreb index

All Science Journal Classification (ASJC) codes

General Mathematics

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https://doi.org/10.5269/bspm.v37i2.29148

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title = "A short note on Hyper Zagreb Index",

abstract = "In this paper, we present and analyze the upper and lower bounds on the Hyper-Zagreb index χ2(G) of graph G in terms of the number of vertices (n), number of edges (m), maximum degree (∆), minimum degree (δ) and the inverse degree (ID(G)). In addition, a counter example on the upper bound of the second Zagreb index for Theorems 2.2 and 2.4 from_ [20] is provided. Finally, we present the lower and upper bounds on χ2(G) + χ2(G), where G denotes the complement of G.",

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AU - Mansour, Toufik

AU - Rostami, Mohammad Ali

AU - Xavier, G. B.A.

N1 - Publisher Copyright: © Soc. Paran. de Mat.

PY - 2019

Y1 - 2019

N2 - In this paper, we present and analyze the upper and lower bounds on the Hyper-Zagreb index χ2(G) of graph G in terms of the number of vertices (n), number of edges (m), maximum degree (∆), minimum degree (δ) and the inverse degree (ID(G)). In addition, a counter example on the upper bound of the second Zagreb index for Theorems 2.2 and 2.4 from_ [20] is provided. Finally, we present the lower and upper bounds on χ2(G) + χ2(G), where G denotes the complement of G.

AB - In this paper, we present and analyze the upper and lower bounds on the Hyper-Zagreb index χ2(G) of graph G in terms of the number of vertices (n), number of edges (m), maximum degree (∆), minimum degree (δ) and the inverse degree (ID(G)). In addition, a counter example on the upper bound of the second Zagreb index for Theorems 2.2 and 2.4 from_ [20] is provided. Finally, we present the lower and upper bounds on χ2(G) + χ2(G), where G denotes the complement of G.

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A short note on Hyper Zagreb Index

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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