Constructably Laplacian integral graphs |
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Authors: | Steve Kirkland |
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Institution: | Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada S4S 0A2 |
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Abstract: | A graph is Laplacian integral if the spectrum of its Laplacian matrix consists entirely of integers. We consider the class of constructably Laplacian integral graphs - those graphs that be constructed from an empty graph by adding a sequence of edges in such a way that each time a new edge is added, the resulting graph is Laplacian integral. We characterize the constructably Laplacian integral graphs in terms of certain forbidden vertex-induced subgraphs, and consider the number of nonisomorphic Laplacian integral graphs that can be constructed by adding a suitable edge to a constructably Laplacian integral graph. We also discuss the eigenvalues of constructably Laplacian integral graphs, and identify families of isospectral nonisomorphic graphs within the class. |
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Keywords: | 05C50 15A18 |
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