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.

Title

Hebron University Research Journal(A). Vol.(6), pp.(35–46)

Publisher

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Publisher Country

Palestine

Publication Type

Both (Printed and Online)

Volume

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Year

2012

Pages

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