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HUB ZAGREB ENERGY OF GRAPHS
Keywords:
hub degree, hub Zagreb matrix, hub Zagreb energy, hub Zagreb indices.DOI:
https://doi.org/10.17654/0974165823068Abstract
Let $G$ be a graph of order $n$ with vertices labeled as $v_1, v_2, \ldots, v_n$. Let $d_{h_i}$ be the hub degree of the vertex $v_i$ for $i=1,2, \ldots, n$. In this paper, we introduce the first hub Zagreb matrix and second hub Zagreb matrix of $G$. The first hub Zagreb matrix of $G$ is the square matrix of order $n$ whose $i j$ th-entry is equal to $d_{h_i}+d_{h_j}$ if $v_i$ is adjacent to $v_j$ and zero otherwise. We further define first hub Zagreb energy and investigate its nature based on the eigenvalues of the first hub Zagreb matrix. In addition, we establish some bounds to first hub Zagreb energy in terms of hub Zagreb index and hyper-hub Zagreb index and calculate the hub Zagreb energy of hydrocarbons.
Received: August 10, 2023
Accepted: November 9, 2023
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