Note on the Reformulated Zagreb Indices of Two Classes of Graphs

Note on the Reformulated Zagreb Indices of Two Classes of Graphs

The reformulated Zagreb indices of a graph are obtained from the original Zagreb indices by replacing vertex degrees with edge degrees, where the degree of an edge is taken as the sum of degrees of its two end vertices minus 2. In this paper, we obtain two upper bounds of the first reformulated Zagr...

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Main Authors: Tongkun Qu, Mengya He, Shengjin Ji, Xia Li
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Chemistry
Online Access:http://dx.doi.org/10.1155/2020/4860327
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spelling doaj-ba8609e797e74b398c61fb773fa0f93a2020-11-25T02:38:45ZengHindawi LimitedJournal of Chemistry2090-90632090-90712020-01-01202010.1155/2020/48603274860327Note on the Reformulated Zagreb Indices of Two Classes of GraphsTongkun Qu0Mengya He1Shengjin Ji2Xia Li3School of Science, Shandong University of Technology, Zibo, Shandong 255000, ChinaSchool of Science, Shandong University of Technology, Zibo, Shandong 255000, ChinaSchool of Science, Shandong University of Technology, Zibo, Shandong 255000, ChinaSchool of Science, Shandong University of Technology, Zibo, Shandong 255000, ChinaThe reformulated Zagreb indices of a graph are obtained from the original Zagreb indices by replacing vertex degrees with edge degrees, where the degree of an edge is taken as the sum of degrees of its two end vertices minus 2. In this paper, we obtain two upper bounds of the first reformulated Zagreb index among all graphs with p pendant vertices and all graphs having key vertices for which they will become trees after deleting their one key vertex. Moreover, the corresponding extremal graphs which attained these bounds are characterized.http://dx.doi.org/10.1155/2020/4860327
collection DOAJ
language English
format Article
sources DOAJ
author Tongkun Qu
Mengya He
Shengjin Ji
Xia Li
spellingShingle Tongkun Qu
Mengya He
Shengjin Ji
Xia Li
Note on the Reformulated Zagreb Indices of Two Classes of Graphs
Journal of Chemistry
author_facet Tongkun Qu
Mengya He
Shengjin Ji
Xia Li
author_sort Tongkun Qu
title Note on the Reformulated Zagreb Indices of Two Classes of Graphs
title_short Note on the Reformulated Zagreb Indices of Two Classes of Graphs
title_full Note on the Reformulated Zagreb Indices of Two Classes of Graphs
title_fullStr Note on the Reformulated Zagreb Indices of Two Classes of Graphs
title_full_unstemmed Note on the Reformulated Zagreb Indices of Two Classes of Graphs
title_sort note on the reformulated zagreb indices of two classes of graphs
publisher Hindawi Limited
series Journal of Chemistry
issn 2090-9063
2090-9071
publishDate 2020-01-01
description The reformulated Zagreb indices of a graph are obtained from the original Zagreb indices by replacing vertex degrees with edge degrees, where the degree of an edge is taken as the sum of degrees of its two end vertices minus 2. In this paper, we obtain two upper bounds of the first reformulated Zagreb index among all graphs with p pendant vertices and all graphs having key vertices for which they will become trees after deleting their one key vertex. Moreover, the corresponding extremal graphs which attained these bounds are characterized.
url http://dx.doi.org/10.1155/2020/4860327
work_keys_str_mv AT tongkunqu noteonthereformulatedzagrebindicesoftwoclassesofgraphs
AT mengyahe noteonthereformulatedzagrebindicesoftwoclassesofgraphs
AT shengjinji noteonthereformulatedzagrebindicesoftwoclassesofgraphs
AT xiali noteonthereformulatedzagrebindicesoftwoclassesofgraphs
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