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Title: Graphs that have a weighted adjacency matrix with spectrum {λn−21,λ21}
Authors: Meagher, Karen
Sciriha, Irene
Keywords: Eigenvalues
Mathematics -- Problems, exercises, etc.
Mathematics -- Charts, diagrams, etc.
Issue Date: 2015
Publisher: Cornell University
Citation: Meagher, K., & Sciriha, I. (2015). Graphs that have a weighted adjacency matrix with spectrum {λn−21,λ21}. arXiv preprint arXiv:1504.04178.
Abstract: In this paper we completely characterize the graphs which have an edge weighted adjacency matrix belonging to the class of n×n involutions with spectrum equal to {λn−2/1,λ2/2} for some λ1 and some λ2. The connected graphs turn out to be the cographs constructed as the join of at least two unions of pairs of complete graphs, and possibly joined with one other complete graph.
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