First zagreb spectral radius of unicyclic graphs and trees

期刊论文
发表日期：

2024年7月30日

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Parikshit Das,
Kinkar Chandra Das,
Sourav Mondal,
Anita Pal

摘要

In light of the successful investigation of the adjacency matrix, a significant amount of its modification is observed employing numerous topological indices. The matrix corresponding to the well-known first Zagreb index is one of them. The entries of the first Zagreb matrix are $d_{u_i}+d_{u_j}$ $d_{u_{i}} + d_{u_{j}}$ , if $u_i$ $u_{i}$ is connected to $u_j$ $u_{j}$ ; 0, otherwise, where $d_{u_i}$ $d_{u_{i}}$ is degree of i-th vertex. The current work is concerned with the mathematical properties and chemical significance of the spectral radius ( $\rho _1$ $ρ_{1}$ ) associated with this matrix. The lower and upper bounds of $\rho _1$ $ρ_{1}$ are computed with characterizing extremal graphs for the class of unicyclic graphs and trees. The chemical connection of the first Zagreb spectral radius is established by exploring its role as a structural descriptor of molecules. The isomer discrimination ability of $\rho _1$ $ρ_{1}$ is also explained.