Reformulated Zagreb Indices of Trees

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Dehgardi Nasrin

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Journal Paper

Paper Information

Journal: Mathematics Interdisciplinary Research Year:2024 | Volume:9 | Issue:4 Page(s): 373-383

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Information Journal Paper

Title

Reformulated Zagreb Indices of Trees

Author(s)

Dehgardi Nasrin | Issue Writer Certificate

Keywords

Tree‎

‎Zagreb indices‎

‎First and second reformulated Zagreb indices

Abstract

‎Zagreb indices were reformulated in terms of the edge degrees instead of the vertex degrees‎. For a graph $G$‎, ‎the first and second reformulated Zagreb indices are defined respectively as‎:‎$$EM_1(G)=\sum_{\varepsilon\in E(G)}d^2(\varepsilon), EM_2(G)=\sum_{\varepsilon,\varepsilon'\in E(G),\,\varepsilon\sim \varepsilon'}d(\varepsilon)\,d(\varepsilon'),$$‎ where $d(\varepsilon)$ and $d(\varepsilon')$ denote the degree of the edges $\varepsilon$ and $\varepsilon'$ respectively‎, ‎and $\varepsilon\sim \varepsilon'$ means that the edges $\varepsilon$ and $\varepsilon'$ are adjacent‎. In this paper‎, ‎we obtain sharp lower bounds on the first and second reformulated Zagreb‎ indices with a given number of vertices and maximum degree‎. ‎Furthermore‎, ‎we will determine the extremal trees that achieve these lower bounds‎.

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