On Randić Energy of Graphs

Kinkar Ch Das; Sezer Sorgun

On Randić Energy of Graphs

Kinkar Ch Das, Sezer Sorgun

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

80 Scopus citations

Abstract

Let G = (V, E) be a simple graph with vertex set V (G) = {v₁, v₂, …, v_n} and edge set E(G). The Randić matrix R = (r_ij) of a graph G whose vertex v_i has degree d_i is defined by r_ij = 1/√d_i d_j if the vertices v_i and v_j are adjacent and r_ij = 0 otherwise. The Randić energy RE is the sum of absolute values of the eigenvalues of R. We provide lower and upper bounds for RE in terms of no. of vertices, maximum degree, minimum degree and the determinant of the adjacency matrix of graphs G.

Original language	English
Pages (from-to)	227-238
Number of pages	12
Journal	Match
Volume	72
Issue number	1
State	Published - 2014

Cite this

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abstract = "Let G = (V, E) be a simple graph with vertex set V (G) = \{v1, v2, …, vn\} and edge set E(G). The Randi{\'c} matrix R = (rij) of a graph G whose vertex vi has degree di is defined by rij = 1/√di dj if the vertices vi and vj are adjacent and rij = 0 otherwise. The Randi{\'c} energy RE is the sum of absolute values of the eigenvalues of R. We provide lower and upper bounds for RE in terms of no. of vertices, maximum degree, minimum degree and the determinant of the adjacency matrix of graphs G.",

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N2 - Let G = (V, E) be a simple graph with vertex set V (G) = {v1, v2, …, vn} and edge set E(G). The Randić matrix R = (rij) of a graph G whose vertex vi has degree di is defined by rij = 1/√di dj if the vertices vi and vj are adjacent and rij = 0 otherwise. The Randić energy RE is the sum of absolute values of the eigenvalues of R. We provide lower and upper bounds for RE in terms of no. of vertices, maximum degree, minimum degree and the determinant of the adjacency matrix of graphs G.

AB - Let G = (V, E) be a simple graph with vertex set V (G) = {v1, v2, …, vn} and edge set E(G). The Randić matrix R = (rij) of a graph G whose vertex vi has degree di is defined by rij = 1/√di dj if the vertices vi and vj are adjacent and rij = 0 otherwise. The Randić energy RE is the sum of absolute values of the eigenvalues of R. We provide lower and upper bounds for RE in terms of no. of vertices, maximum degree, minimum degree and the determinant of the adjacency matrix of graphs G.

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On Randić Energy of Graphs

Abstract

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