Abstract

The Rancho spread of a simple undirected graph G, spr(R)(G), is equal to the maximal difference between two eigenvalues of the Rancho matrix, disregarding the spectral radius [Comes et al., MATCH Commun. Math. Comput. Chem. 72 (2014) 249-266]. Using a rank-one perturbation on the Randic matrix of G it is obtained a new matrix whose matricial spread coincide with spr(R)(G). By means of this result, upper bounds for spr(R)(G) are obtained.