GENERAL RANDIC MATRIX AND GENERAL RANDIC ENERGY

Let g be a simple graph with vertex set v (g) = fv1; v2; : : : ; vng and di the degree of itsvertex vi, i = 1; 2; : : : ; n. inspired by the randic matrix and the general randic index of a graph, weintroduce the concept of general randic matrix r of g, which is dened by (r)i;j = (didj) if viand vj are adjacent, and zero otherwise. similarly, the general randic eigenvalues are the eigenvaluesof the general randic matrix, the greatest general randic eigenvalue is the general randic spectralradius of g, and the general randic energy is the sum of the absolute values of the general randiceigenvalues. in this paper, we prove some properties of the general randic matrix and obtain lower andupper bounds for general randic energy, also, we get some lower bounds for general randic spectralradius of a connected graph. moreover, we give a new sharp upper bound for the general randic energywhen  = ??1=2.