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Neighborhood First Zagreb Index and Maximal Unicyclic and Bicyclic Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 شهریور 1403 اصل مقاله (585.69 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29450.2000 | ||
| نویسندگان | ||
| Waheed Khalid؛ Shamaila Yousaf* | ||
| Department of Mathematics , University of Gujrat, Hafiz Hayat Campus, Gujrat, Pakistan | ||
| چکیده | ||
| 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 $NM_{1}$. | ||
| کلیدواژه‌ها | ||
| extremal graph theory؛ neighborhood topological index؛ different classes of graphs | ||
| مراجع | ||
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