HUB ZAGREB ENERGY OF GRAPHS
Let G be a graph of order n with vertices labeled as v1, v2, ... vn. Let be the hub degree of the vertex vi for i = 1, 2, ..., 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 ijth-entry is equal to if vi is adjacent to vj 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.
hub degree, hub Zagreb matrix, hub Zagreb energy, hub Zagreb indices.
Received: August 10, 2023; Accepted: November 9, 2023; Published: November 28, 2023
How to cite this article: Veena Mathad and Anand, Hub Zagreb energy of graphs, Advances and Applications in Discrete Mathematics 40(2) (2023), 225-245. http://dx.doi.org/10.17654/0974165823068
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
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