Please use this identifier to cite or link to this item: https://www.um.edu.mt/library/oar/handle/123456789/28171
Title: Graphs with a common eigenvalue deck
Authors: Sciriha, Irene
Keywords: Mathematics -- Charts, diagrams, etc.
Eigenvectors
Mathematics -- Problems, exercises, etc.
Issue Date: 2009
Publisher: Elsevier Inc.
Citation: Sciriha, I. (2009). Graphs with a common eigenvalue deck. Linear Algebra and its Applications, 430(1), 78-85.
Abstract: In this paper, we consider graphs whose deck consists of cards (which are the vertex-deleted subgraphs) that share the same eigenvalue, say μ. We show that, the characteristic polynomial can be reconstructed from the deck, providing a new proof of Tutte’s result for this class of graphs. Moreover, for the subclass of non-singular graphs, the graph can be uniquely reconstructed from the eigenvectors of the cards associated with the eigenvalue μ. The remaining graphs in this class are shown to be μ-cores graphs.
URI: https://www.um.edu.mt/library/oar//handle/123456789/28171
Appears in Collections:Scholarly Works - FacSciMat

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