The spectral graph theory is concerned with the relationship between the spectra of specific matrices associated with a graph and the structural properties of that graph. This paper introduces a general symmetric degree adjacency of a graph G, general symmetric degree of a graph G, and complete weighted graph of a graph. Here we explore its characteristic polynomial using Sachs theorem. We also investigate the bounds for index and energy of general symmetric degree adjacency of a graph. We give two algorithms, first one to find general symmetric degree adjacency of a graph G and second one to find general symmetric degree of a graph G.

general symmetric degree adjacency of G, general symmetric degree of G, characteristic polynomial of G_SDA(G) and G_SD(G), G_SDA(G) and G_SD(G)-eigenvalues, E_a(G), E_g(G).

Received: February 14, 2024; Revised: September 14, 2024; Accepted: October 1, 2024; Published: October 16, 2024

How to cite this article: Jyoti Macha, Sumedha S. Shinde and Prema Sunkad, The general symmetric degree and general symmetric degree adjacency polynomial of a graph and its energy, Advances and Applications in Discrete Mathematics 41(8) (2024), 641-661. https://doi.org/10.17654/0974165824041

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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