The Characteristic Polynomial of a Graph is Reconstructible from the Characteristic Polynomials of its Vertex-Deleted Subgraphs

The question of whether the characteristic polynomial of a simple graph is uniquely determined by the characteristic polynomials of its vertex-deleted subgraphs is one of the many unresolved problems in graph reconstruction. In this paper we prove that the characteristic polynomial of a graph is reconstructible from the characteristic polynomials of the vertex-deleted subgraphs of the graph and its complement. AMS Classification Numbers: 05C60, 05C50

• Type: Journal
• Year: 2000
• Where: COMBINATORICS
• Authors: Elias M. Hagos
• Keywords: Characteristic Polynomials, COMBINATORICS 2000, Simple Graph, Vertex-deleted Subgraphs