Abstract:Two graphs are said to be generalized cospectral if they have the same characteristic polynomials and so do their complements. A graph is controllable if its walk matrix is nonsingular; equivalently, if all the eigenvalues of its adjacency matrix are simple and main. A graph $H$ on $(n+1)$ vertices is an overgraph of another graph $G$ on $n$ vertices if $G$ is a vertex-deleted subgraph of $H$. We prove that no two distinct overgraphs of a controllable graph are generalized cospectral; this strengthens an earli… Show more
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