A generalization and proof of the Aanderaa-Rosenberg conjecture
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Lower bounds to randomized algorithms for graph properties
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Testing whether a digraph contains H-free k-induced subgraphs
Theoretical Computer Science
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An open problem, posed by A. Rosenberg [R], motivates the consideration of representations of graphs and the effect of these representations on the efficiency of algorithms which determine properties of unlabelled graphs. In this paper we investigate three matrix representations of graphs; the (vertex) adjacency matrix, the edge-adjacency matrix, and the incidence matrix. With the exception of one instance of the edge-adjacency matrix, these structures determine an unlabelled graph up to isomorphism and are, as a result, natural candidates for computer representations of graphs.