Path spectra for trees |
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Authors: | Guantao Chen Ralph J Faudree |
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Institution: | a Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, United Statesb Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, United Statesc 3110 Morewood Ln, Charlottesville, VA 22901, United States |
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Abstract: | The path spectrum of a graph is the set of lengths of all maximal paths in the graph. A set S of positive integers is spectral if it is the path spectrum of a tree. We characterize the spectral sets containing at most two odd integers (and arbitrarily many even ones) and obtain several necessary conditions for a set to be spectral. We show that for each even integer s≥2 at least 1/4 of all subsets of the set {2,3,…,s} are spectral and conjecture that all the subsets with at least 3s/4 integers are spectral. |
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Keywords: | Maximal path Tree Path spectrum |
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