Randi ́c Energy and Randi ́c Estrada Index of a Graph

Ş. Burcu Bozkurt, Durmuş Bozkurt

Abstract

Let G be a simple connected graph with n vertices and let d be the degree of its i-th vertex. The Randi ́c matrix of G is the square matrix of order n whose i, j -entry is equal to 1/ di dj if the i-th and j-th vertex of G are adjacent, and zero otherwise. The Randi ́c eigenvalues are the eigenvalues of the Randi ́c matrix. The Randi ́c energy is the sum of the absolute values of the Randi ́c eigenvalues. In this paper, we introduce a new index of the graph G which is called Randi ́c Estrada index. In addition, we obtain lower and upper bounds for the Randi ́c energy and the Randi ́c Estrada index of G. 

Keywords

Randi ́c Matrix, Randi ́c Eigenvalue, Randi ́c Energy, Randi ́c Estrada Index

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