Coefficients of Randic and Sombor characteristic polynomials of some graph types

Year 2022, Volume: 71 Issue: 3, 778 - 790, 30.09.2022

Mert Sinan Oz

https://doi.org/10.31801/cfsuasmas.1080426

Abstract

Let $G$ be a graph. The energy of $G$ is defined as the summation of absolute values of the eigenvalues of the adjacency matrix of $G$. It is possible to study several types of graph energy originating from defining various adjacency matrices defined by correspondingly different types of graph invariants. The first step is computing the characteristic polynomial of the defined adjacency matrix of $G$ for obtaining the corresponding energy of $G$. In this paper, formulae for the coefficients of the characteristic polynomials of both the Randic and the Sombor adjacency matrices of path graph $P_n$ , cycle graph $C_n$ are presented. Moreover, we obtain the five coefficients of the characteristic polynomials of both Randic and Sombor adjacency matrices of a special type of 3−regular graph $R_n$.

Keywords

Graphs, Randic matrix, Sombor matrix, paths, cycles, adjacency

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