An Efficient Algorithm for Graph Isomorphism
Journal of the ACM (JACM)
A Linear Time Algorithm for Deciding Interval Graph Isomorphism
Journal of the ACM (JACM)
Isomorphism of graphs with bounded eigenvalue multiplicity
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
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For a graph G, a graph recurrence sequence x0, x1, x2,... of vectors is defined by the recurrence xt+1 = Axt, t = 0, 1,...., where A is the adjacency matrix of G and x0 is an initial vector. Each vector in this sequence can be thought of as a vertex labeling of G, the label at a given vertex at step t+1 obtained by summing the values at the adjacent vertices at step t. Based on graphical sequences, three concepts are defined: (1) for a graph to be determined by a set of vectors, (2) for two graphs to be m-equivalent, and (3) for the vertices of the graph to be separated by a set of vectors. Results concerning these notions are given, relations to the graph isomorphism problem are discussed, and numerous open problems are posed.