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We present an algorithm for constructing the characteristic polynomial of a threshold graph’s adjacency matrix. The algorithm is based on a diagonalization procedure that is easy to describe. It can be implemented using O(n) space and with running time O(n). Submitted: December 2013 Reviewed: October 2014 Revised: November 2014 Accepted: December 2014(More)
Wedevelop an algorithm for computing the characteristic polynomial ofmatrices related to threshold graphs. We use this as tool to exhibit, for any natural number n ≥ 4, 2n−4 graphs with n vertices that have a non isomorphic pair with the same signless Laplacian spectrum. We also show how to construct infinite families of pairs of non isomorphic graphs(More)
The Laplacian and normalized Laplacian energy of G are given by expressions EL(G) = ∑n i=1 |μi − d|, EL(G) = ∑n i=1 |λi − 1|, respectively, where μi and λi are the eigenvalues of Laplacian matrix L and normalized Laplacian matrix L of G. An interesting problem in spectral graph theory is to find graphs {L,L}−noncospectral with the same E{L,L}(G). In this(More)
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