Recent Advancements in Graph Theory

30Randić Energy of Some Graphs

S. K. Vaidya

Saurashtra University,Rajkot-360005,Gujarat(India).E-mail: [e-mail]

G. K. Rathod

V.V.P. Engineering College,Rajkot-360005,Gujarat(India).Email: [e-mail]

Let d_i be the degrees of vertices v_i, i = 1, 2, …, n of graph G; then the Randić matrix R(G) of graph G is an n × n matrix whose entries are given by rij=1/didj, if the vertices v_i and v_j are adjacent in G and 0 otherwise. The energy of the graph G is defined to be the sum of absolute values of eigenvalues of R(G). Here,we explore this concept for extended m-shadow, extended m-splitting, double cover and extended double cover of graph G.

30.1Introduction

Let G be a simple connected undirected graph with v₁, v₂, …, ...