New bounds on the hyper-Zagreb index for the simple connected graphs

Suresh Elumalai; Toufik Mansour; Mohammad Ali Rostami

doi:https://doi.org/10.5614/ejgta.2018.6.1.12

New bounds on the hyper-Zagreb index for the simple connected graphs

Suresh Elumalai, Toufik Mansour, Mohammad Ali Rostami

Department of Mathematics

University of Haifa

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

Abstract

The hyper-Zagreb index of a simple connected graph G is defined by. In this paper, we establish, analyze and compare some new upper bounds on the Hyper-Zagreb index in terms of the number of vertices (n), number of edges (m), maximum vertex degree (Δ), and minimum vertex degree (δ), first Zagreb index M₁(G), second Zagreb index M₂(G), harmonic index H(G), and inverse edge degree IED(G). In addition, we give the identities on Hyper-Zagreb index and its coindex for the simple connected graphs.

Original language	American English
Pages (from-to)	166-177
Number of pages	12
Journal	Electronic Journal of Graph Theory and Applications
Volume	6
Issue number	1
DOIs	https://doi.org/10.5614/ejgta.2018.6.1.12
State	Published - 2018

Keywords

Forgotten index
Hyper-zagreb index
Zagreb indices

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

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https://doi.org/10.5614/ejgta.2018.6.1.12

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title = "New bounds on the hyper-Zagreb index for the simple connected graphs",

abstract = "The hyper-Zagreb index of a simple connected graph G is defined by. In this paper, we establish, analyze and compare some new upper bounds on the Hyper-Zagreb index in terms of the number of vertices (n), number of edges (m), maximum vertex degree (Δ), and minimum vertex degree (δ), first Zagreb index M1(G), second Zagreb index M2(G), harmonic index H(G), and inverse edge degree IED(G). In addition, we give the identities on Hyper-Zagreb index and its coindex for the simple connected graphs.",

keywords = "Forgotten index, Hyper-zagreb index, Zagreb indices",

author = "Suresh Elumalai and Toufik Mansour and Rostami, {Mohammad Ali}",

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doi = "https://doi.org/10.5614/ejgta.2018.6.1.12",

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AU - Mansour, Toufik

AU - Rostami, Mohammad Ali

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N2 - The hyper-Zagreb index of a simple connected graph G is defined by. In this paper, we establish, analyze and compare some new upper bounds on the Hyper-Zagreb index in terms of the number of vertices (n), number of edges (m), maximum vertex degree (Δ), and minimum vertex degree (δ), first Zagreb index M1(G), second Zagreb index M2(G), harmonic index H(G), and inverse edge degree IED(G). In addition, we give the identities on Hyper-Zagreb index and its coindex for the simple connected graphs.

AB - The hyper-Zagreb index of a simple connected graph G is defined by. In this paper, we establish, analyze and compare some new upper bounds on the Hyper-Zagreb index in terms of the number of vertices (n), number of edges (m), maximum vertex degree (Δ), and minimum vertex degree (δ), first Zagreb index M1(G), second Zagreb index M2(G), harmonic index H(G), and inverse edge degree IED(G). In addition, we give the identities on Hyper-Zagreb index and its coindex for the simple connected graphs.

KW - Forgotten index

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KW - Zagreb indices

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JO - Electronic Journal of Graph Theory and Applications

JF - Electronic Journal of Graph Theory and Applications

IS - 1

ER -

New bounds on the hyper-Zagreb index for the simple connected graphs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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