An-Najah Staff

This paper Deals with the complete bipartite graph K(r, n-r) and the cycle Cn.  The matrix of concern is the matrix B which is the (n, n) matrix and whose non zero entries are the reciprocals of the non zero entries of the distance matrix D.  A complete characterization of the spectrum of B and a set of n independent eigenvectors of B will be presented.  Two special cases will be mentioned, namely the star K(1, n-1) and the graph K(2, n-2). We will also look at the case of infinite graph, i. e if the size  n  grows big while r  stays finite.  Finally, some numerical data will be presented.  As for the cycle, we present the complete set of eigenvalues of the matrix B.