Advances and Applications in Discrete Mathematics

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THE GENERAL SYMMETRIC DEGREE AND GENERAL SYMMETRIC DEGREE ADJACENCY POLYNOMIAL OF A GRAPH AND ITS ENERGY

Authors

  • Jyoti Macha
  • Sumedha S. Shinde
  • Prema Sunkad

Keywords:

Keywords and phrases: general symmetric degree adjacency of $G$, general symmetric degree of $G$, characteristic polynomial of $G_{S D} A(G)$ and $G_{S D}(G), G_{S D} A(G)$ and $G_{S D}(G)$ eigenvalues, $\mathbb{E}_a(G), \mathbb{E}_g(G)$

DOI:

https://doi.org/10.17654/0974165824041

Abstract

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.

Received: February 14, 2024
Revised: September 14, 2024
Accepted: October 1, 2024

References

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Published

2024-10-16

Issue

Vol. 41 No. 8 (2024)

Section

Articles

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How to Cite

THE GENERAL SYMMETRIC DEGREE AND GENERAL SYMMETRIC DEGREE ADJACENCY POLYNOMIAL OF A GRAPH AND ITS ENERGY. (2024). Advances and Applications in Discrete Mathematics, 41(8), 641-661. https://doi.org/10.17654/0974165824041

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