Neighborhood first Zagreb index and maximal unicyclic and bicyclic graphs

Document Type : Original paper

Authors

Department of Mathematics , University of Gujrat, Hafiz Hayat Campus, Gujrat, Pakistan

Abstract

The Neighborhood First Zagreb Index $NM_{1}$ measures the topological properties of a molecular graph. Neighborhood First Zagreb Index $NM_{1}$ is defined as $NM_{1}(G) = \sum_{ v\in V (G)}(S(v))^{2}$, where $S(v)$ used to represent the sum of degrees of vertices adjacent to a vertex $v$ in a graph $G$.  In this study, we focus on characterizing the graphs with the maximum neighborhood first Zagreb index in the class of unicyclic/bicyclic graphs on $n$ vertices, where $n$ is a fixed integer greater than or equal to $5$. Specifically, we are interested in identifying the graphs that have the highest value according to the recently introduced neighborhood first Zagreb index $NM_{1}$.

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References

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Communications in Combinatorics and Optimization
Volume 11, Issue 2
June 2026
Pages 563-580

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