Article ID Journal Published Year Pages File Type
4602169 Linear Algebra and its Applications 2009 8 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory