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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Bibliographic Details
Published in:Journal of chemistry 2020-02, Vol.2020 (2020), p.1-4
Main Authors: Li, Xia, Ji, Shengjin, He, Mengya, Qu, Tongkun
Format: Article
Language:English
Subjects:
Apexes
Applied mathematics
Chemistry
Combinatorics
Connectivity
Graph theory
Graphs
Trees (mathematics)
Upper bounds
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Summary: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.
ISSN:2090-9063
2090-9071
DOI:10.1155/2020/4860327