Cospectral bipartite graphs for the normalized Laplacian

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2013-01-01
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Osborne, Steven
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Leslie Hogben
Steven Butler
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Mathematics
Abstract

We present an infinite example of trees cospectral with respect to the normalized Laplacian and a use of the weighted normalized Laplacian to find cospectral pairs of unweighted bipartite graphs with respect to the normalized Laplacian. We show that almost all trees are cospectral with respect to the normalized Laplacian. Further, we show that almost all trees are cospectral with respect to the generalized characteristic polynomial. This would imply that almost all trees T have a mate T' such that T and T' are simultaneously cospectral with respect to all of the adjacency, (signless) Laplacian, and normalized Laplacian matrices.

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Tue Jan 01 00:00:00 UTC 2013