Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

General Randić matrix and general Randić incidence matrix

Language

English

Abstract

© 2015 Elsevier B.V. All rights reserved. Let G be a connected graph with vertex set V(G) = {v1,⋯, vn} and edge set E(G) = {e1,⋯, em}. Let di be the degree of the vertex νi. The general Randić matrix Rα = ((Rα)ij)n×n of G is defined by (Rα)ij = (didj)α if vertices νi and νj are adjacent in G and 0 otherwise. The Randić signless Laplacian matrix Qα = D2α+1 + Rα, where α is a nonzero real number and D is the degree diagonal matrix of G. The general Randić energy REα is the sum of absolute values of the eigenvalues of Rα. The general Randić incidence matrix B = ((B)ij)n×m of a graph G is defined by (B)ij = dαi if νi is incident to ej and 0 otherwise. Naturally, the general Randić incidence energy BEα is the sum of the singular values of B. In this paper, we investigate the connected graphs with s distinct Rα-eigenvalues, where 2 ≤ s ≤ n. Moreover, we establish the relation between the Randić signless Laplacian eigenvalues of G and the general Randić energy of its subdivided graph S (G). Also we give lower and upper bounds on the general Randić incidence energy. Finally, the general Randić incidence energy of a graph and that of its subgraphs are compared.

Keywords

General Randić energy, General Randić incidence energy, General Randić incidence matrix, General Randić matrix

Publication Date

2015

Source Publication Title

Discrete Applied Mathematics

Volume

186

Start Page

168

End Page

175

Publisher

Elsevier

DOI

10.1016/j.dam.2015.01.029

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.dam.2015.01.029

ISSN (print)

0166218X

This document is currently not available here.

Share

COinS