GENERAL RANDI´C ENERGY OF SOME GRAPHS

Abstract

For a graph G of order n, the general Randi´c matrix GR(G) = [gij ] is a symmetric matrix of order n in which gij = (didj)α, α ∈ R if the vertices vi and vj are adjacent in G and 0, otherwise, where di is the degree of vertex vi. The general Randi´c energy EGR(G) of G is the sum of the absolute values of the eigenvalues of GR(G). In this paper, we compute the general Randi´c energy of the line graph of regular graph and the graph obtained by duplication of graph elements for regular graph. We also investigate general Randi´c equienergetic graphs