More on inverse degree and topological indices of graphs

Suresh Elumalai; Sunilkumar M. Hosamani; Toufik Mansour; Mohammad Ali Rostami

doi:10.2298/FIL1801165E

More on inverse degree and topological indices of graphs

Suresh Elumalai, Sunilkumar M. Hosamani, Toufik Mansour, Mohammad Ali Rostami

Department of Mathematics

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

Abstract

The inverse degree of a graph G with no isolated vertices is defined as the sum of reciprocal of vertex degrees of the graph G. In this paper, we obtain several lower and upper bounds on inverse degree ID(G). Moreover, using computational results, we prove our upper bound is strong and has the smallest deviation from the inverse degree ID(G). Next, we compare inverse degree ID(G) with topological indices (Randić index R(G), geometric-arithmetic index GA(G)) for chemical trees and also we determine the n−vertex chemical trees with the minimum, the second and the third minimum, as well as the second and the third maximum of ID − R. In addition, we correct the second and third minimum Randić index chemical trees in [16].

Original language	English
Pages (from-to)	165-178
Number of pages	14
Journal	Filomat
Volume	32
Issue number	1
DOIs	https://doi.org/10.2298/FIL1801165E
State	Published - 2018

Bibliographical note

Funding Information:
2010 Mathematics Subject Classification. Primary 05C07 (mandatory); Secondary 05C35, 05C90 (optionally) Keywords. First Zagreb index, Second Zagreb index, Inverse degree Received: 20 February 2017; Accepted: 31 July 2017 Communicated by Paola Bonacini bResearch supported by the Science and Engineering Research Board, New Delhi, India. (SERB/F/4168/2012-13) Email addresses: sureshkako@gmail.com, Corresponding Author (Suresh Elumalai), sunilkumar.rcu@gmail.com (Sunilkumar M. Hosamani), tmansour@univ.haifa.ac.il (Toufik Mansour), a.rostami@uni-jena.de (Mohammad Ali Rostami)

Funding Information:
Research supported by the Science and Engineering Research Board, New Delhi, India. (SERB/F/4168/2012-13) The authors would like to give sincere gratitude the unknown reviewers for careful reading of the manuscript and for valuable comments, which greatly improved quality of our paper. The first author would like to thank his beloved Professor Kinkar Ch. Das for sending us his paper and the kind support.

Publisher Copyright:
© 2018, University of Nis. All rights reserved.

Keywords

First Zagreb index
Inverse degree
Second Zagreb index

ASJC Scopus subject areas

Mathematics (all)

Access to Document

10.2298/FIL1801165E

Cite this

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title = "More on inverse degree and topological indices of graphs",

abstract = "The inverse degree of a graph G with no isolated vertices is defined as the sum of reciprocal of vertex degrees of the graph G. In this paper, we obtain several lower and upper bounds on inverse degree ID(G). Moreover, using computational results, we prove our upper bound is strong and has the smallest deviation from the inverse degree ID(G). Next, we compare inverse degree ID(G) with topological indices (Randi{\'c} index R(G), geometric-arithmetic index GA(G)) for chemical trees and also we determine the n−vertex chemical trees with the minimum, the second and the third minimum, as well as the second and the third maximum of ID − R. In addition, we correct the second and third minimum Randi{\'c} index chemical trees in [16].",

keywords = "First Zagreb index, Inverse degree, Second Zagreb index",

author = "Suresh Elumalai and Hosamani, {Sunilkumar M.} and Toufik Mansour and Rostami, {Mohammad Ali}",

note = "Funding Information: 2010 Mathematics Subject Classification. Primary 05C07 (mandatory); Secondary 05C35, 05C90 (optionally) Keywords. First Zagreb index, Second Zagreb index, Inverse degree Received: 20 February 2017; Accepted: 31 July 2017 Communicated by Paola Bonacini bResearch supported by the Science and Engineering Research Board, New Delhi, India. (SERB/F/4168/2012-13) Email addresses: sureshkako@gmail.com, Corresponding Author (Suresh Elumalai), sunilkumar.rcu@gmail.com (Sunilkumar M. Hosamani), tmansour@univ.haifa.ac.il (Toufik Mansour), a.rostami@uni-jena.de (Mohammad Ali Rostami) Funding Information: Research supported by the Science and Engineering Research Board, New Delhi, India. (SERB/F/4168/2012-13) The authors would like to give sincere gratitude the unknown reviewers for careful reading of the manuscript and for valuable comments, which greatly improved quality of our paper. The first author would like to thank his beloved Professor Kinkar Ch. Das for sending us his paper and the kind support. Publisher Copyright: {\textcopyright} 2018, University of Nis. All rights reserved.",

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doi = "10.2298/FIL1801165E",

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AU - Elumalai, Suresh

AU - Hosamani, Sunilkumar M.

AU - Mansour, Toufik

AU - Rostami, Mohammad Ali

N1 - Funding Information: 2010 Mathematics Subject Classification. Primary 05C07 (mandatory); Secondary 05C35, 05C90 (optionally) Keywords. First Zagreb index, Second Zagreb index, Inverse degree Received: 20 February 2017; Accepted: 31 July 2017 Communicated by Paola Bonacini bResearch supported by the Science and Engineering Research Board, New Delhi, India. (SERB/F/4168/2012-13) Email addresses: sureshkako@gmail.com, Corresponding Author (Suresh Elumalai), sunilkumar.rcu@gmail.com (Sunilkumar M. Hosamani), tmansour@univ.haifa.ac.il (Toufik Mansour), a.rostami@uni-jena.de (Mohammad Ali Rostami) Funding Information: Research supported by the Science and Engineering Research Board, New Delhi, India. (SERB/F/4168/2012-13) The authors would like to give sincere gratitude the unknown reviewers for careful reading of the manuscript and for valuable comments, which greatly improved quality of our paper. The first author would like to thank his beloved Professor Kinkar Ch. Das for sending us his paper and the kind support. Publisher Copyright: © 2018, University of Nis. All rights reserved.

PY - 2018

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N2 - The inverse degree of a graph G with no isolated vertices is defined as the sum of reciprocal of vertex degrees of the graph G. In this paper, we obtain several lower and upper bounds on inverse degree ID(G). Moreover, using computational results, we prove our upper bound is strong and has the smallest deviation from the inverse degree ID(G). Next, we compare inverse degree ID(G) with topological indices (Randić index R(G), geometric-arithmetic index GA(G)) for chemical trees and also we determine the n−vertex chemical trees with the minimum, the second and the third minimum, as well as the second and the third maximum of ID − R. In addition, we correct the second and third minimum Randić index chemical trees in [16].

AB - The inverse degree of a graph G with no isolated vertices is defined as the sum of reciprocal of vertex degrees of the graph G. In this paper, we obtain several lower and upper bounds on inverse degree ID(G). Moreover, using computational results, we prove our upper bound is strong and has the smallest deviation from the inverse degree ID(G). Next, we compare inverse degree ID(G) with topological indices (Randić index R(G), geometric-arithmetic index GA(G)) for chemical trees and also we determine the n−vertex chemical trees with the minimum, the second and the third minimum, as well as the second and the third maximum of ID − R. In addition, we correct the second and third minimum Randić index chemical trees in [16].

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More on inverse degree and topological indices of graphs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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