We present in this short note a polynomial graph extension procedure that can be used to improve any graph isomorphism algorithm. This construction propagates new constraints from the isomorphism constraints of the input graphs (denoted by G(V,E) and G(V , E)). Thus, information from the edge structures of G and G is ”hashed” into the weighted edges of the extended graphs. A bijective mapping i...

PageRank is a ranking method that assigns scores to web pages using the limit distribution of a random walk on the web graph. A fibration of graphs is a morphism that is a local isomorphism of inneighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. We show that a deep connection relates fibrations and Markov chains with restart, a particular kind o...

Combining the the results of A.R. Meyer and L.J. Stockmeyer " The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space " , and K.S. Booth " Iso-morphism testing for graphs, semigroups, and finite automata are polynomiamlly equivalent problems " shows that graph isomorphism is PSPACE-complete. The equivalence problem for regular expressions was shown to be PSPACE-...

The concepts of separation index of a graph and of a surface are introduced. We prove that the separation index of the sphere is 3. Also the separation index of any graph faithfully embedded in a surface of genus g is bounded by a funtion of g. 2002 Wiley Periodicals, Inc. J Graph Theory 41: 53–61, 2002 1. GRAPH ISOMORPHISM This first section on the Graph Isomorphism Problem is meant only as mo...

The graph isomorphism problem is considered. We assign modified characteristic polynomials for graphs and reduce the graph isomorphism problem to the following one. It is required to find out, is there such an enumeration of the graphs vertices that the polynomials of the graphs are equal. We present algorithms that use the redution and we show that we may check equality of the graphs polynomia...

The complexity of graph isomorphism (GraphIso) is a famous unresolved problem in theoretical computer science. For graphs G and H, it asks whether they are the same up to a relabeling. In 1981, Lubiw proved that list restricted graph isomorphism (ListIso) is NP-complete: for each u ∈ V (G), we are given a list L(u) ⊆ V (H) of possible images of u. After 35 years, we revive the study of this pro...

In a bounded valence graph every vertex has O(1) neighbours. Testing isomorphism of bounded valence graphs is known to be in P [15], something that is not clear to hold for graph isomorphism in general. We show that testing isomorphism for undirected, directed and colored graphs of valence 2 is logspace complete. We also prove the following: If a special version of bounded valence GI is hard fo...

In this paper, we show how isomorphism checking can be used as an effective technique for symmetry reduction. Reduced state spaces are equivalent to the original ones under a strong notion of bisimilarity which preserves the multiplicity of outgoing transitions, and therefore also preserves stochastic temporal logics. We have implemented this in a setting where states are arbitrary graphs. Sinc...

The colored graph isomorphism problem is a restricted version of the general graph isomorphism (GI) problem that involves deciding the existence of a color preserving isomorphism between a pair of colored graphs. In this report, we study this problem for graphs whose color multiplicity is bounded by 3 (3-GI). We begin by formally defining the colored graph isomorphism problem and setup our nota...