Research ArticleNo Access

On the Randić matrix and Randić energy

Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

E-mail Address: hakimehhatefi3@gmail.com

Department of Mathematics, Babol Noshirvani University of Technology, Shariati Avenue, Babol, Postal Code: 47148-71167, I. R. Iran

E-mail Address: ha.ahangar@nit.ac.ir

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R. Khoeilar

Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

E-mail Address: khoeilar@azaruniv.ac.ir

Corresponding author.

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S. M. Sheikholeslami

Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

E-mail Address: s.m.sheikholeslami@azaruniv.ac.ir

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https://doi.org/10.1142/S1793557121501552Cited by:0 (Source: Crossref)

Abstract

Let $G$ $G$ be a graph with $n$ $n$ vertices, and let $d_{u}$ $d_{u}$ be the degree of the vertex $u$ $u$ in the graph $G$ $G$ . The Randić matrix of $G$ $G$ is the square matrix of order $n$ $n$ whose $(i, j)$ $(i, j)$ -entry is equal to ${(d_{u} d_{v})}^{\frac{- 1}{2}}$ ${(d_{u} d_{v})}^{\frac{- 1}{2}}$ if the vertex $u$ $u$ and the vertex $v$ $v$ of $G$ $G$ are adjacent, and $0$ $0$ otherwise. The Randić eigenvalues of $G$ $G$ are the eigenvalues of its Randić matrix and the Randić energy of $G$ $G$ is the sum of the absolute values of its Randić eigenvalues. In this paper, we obtain some new results for the Randić eigenvalues and the Randić energy of a graph.

Communicated by I. Inam

Keywords:

AMSC: 05C50, 15A18, 92E10

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