The question of whether there is a polynomial time algorithm deciding whether two graphs are isomorphic has been a one of the best known open problems in theoretical computer science for more than forty years. Indeed, the graph isomorphism problem is one of the very few natural problems in NP that is neither known to be in P nor known to be NP-complete. The question is still wide open, but a nu...

We study the complexity of the Subgraph Bisimulation Problem, which stands to Graph Bisimulation as Subgraph Isomorphism stands to Graph Isomorphism and we prove its NP-Completeness. Our analysis is motivated by its applications to Semistructured Databases.

Matrix symmetrization and several related problems have an extensive literature, with a recurring ambiguity regarding their complexity status and their relation to graph isomorphism. We present a short survey of these problems to clarify their status. In particular we recall results from the literature showing that matrix symmetrization is in fact NP-hard, while graph isomorphism is still an op...

We consider the Boolean constraint isomorphism problem, that is, the problem of determining whether two sets of Boolean constraint applications can be made equivalent by renaming the variables. We show that depending on the set of allowed constraints, the problem is either coNP-hard and GI-hard, equivalent to graph isomorphism, or polynomial-time solvable. This establishes a complete classifica...

A classical difficult isomorphism testing problem is to test isomorphism of p-groups of class 2 and exponent p in time polynomial in the group order. It is known that this problem can be reduced to solving the alternating matrix space isometry problem over a finite field in time polynomial in the underlying vector space size. We propose a venue of attack for the latter problem by viewing it as ...

We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.

In order to apply canonical labelling of graphs and isomorphism checking in interactive theorem provers, these algorithms must either be mechanically verified or their results verifiable by independent checkers. We analyze a state-of-the-art algorithm for (described McKay Piperno) formulate it terms formal proof system. provide an implementation that can export the obtained graph is form given ...

Abstract We show that every graded ideal of a Leavitt path algebra is isomorphic to algebra. It known I the graph, as generalised hedgehog which defined based on certain sets vertices uniquely determined by . However, this isomorphism may not be graded. replacing short ‘spines’ graph with possibly fewer, but then necessarily longer spines, we obtain (which call porcupine graph) whose Our proof ...