In the past decades for more and more graph classes the Graph Isomorphism Problem was shown to be solvable in polynomial time. An interesting family of graph classes arises from intersection graphs of geometric objects. In this work we show that the Graph Isomorphism Problem for unit square graphs, intersection graphs of axis-parallel unit squares in the plane, can be solved in polynomial time....

We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G ∼= H . For several decades, the np n+O(1) generatorenumeration bound (where p is the smallest prime dividing the order of the group) has been the best worst-case result for general groups. In this work, we show the first improvement over the generator-enumeration boun...

It has been known that the graph isomorphism problem is polynomial-time many-one reducible to the ring isomorphism problem. In fact, two different reductions have already been proposed. For those reductions, rings of certain types have been used to represent a given graph. In this paper, we give yet another reduction, which is based on a simpler and more natural construction of a ring from a gr...

The graph isomorphism problem belongs to the class of NP problems, and has been conjectured intractable, although probably not NP-complete. However, in the context of chemistry, because molecules are a restricted class of graphs, the problem of graph isomorphism can be solved efficiently (i.e., in polynomial-time). This paper presents the theoretical results that for all molecules, the problems...

We investigate a certain condition for isomorphism between circulant graphs (known as the Ad am property) in a stronger form by referring to isospectrality rather than to isomorphism of graphs. We describe a wide class of graphs for which the Ad am conjecture holds. We apply these results to establish an asymptotic formula for the number of non-isomorphic circulant graphs and connected circulan...

Abs t rac t . In graph representations of objects, geometric information is typically lost. This has forced researchers to use graph matching techniques that are intended to handle general graphs. By encoding the lost geometric information into graph representations, however, we can apply more efficient algorithms for constrained graphs. In this paper we introduce an edge ordering property that...

Despite of the fact that graph based methods are gaining more and more popularity in different scientific areas, it has to be considered that the choice of an appropriate algorithm for a given application is still the most crucial task. The lack of a large database of graphs makes the task of comparing the performance of different graph matching algorithms difficult, and often the selection of ...

Biró, Hujter, and Tuza introduced the concept of H-graphs (1992), intersection graphs of connected subgraphs of a subdivision of a graph H. They naturally generalize many important classes of graphs, e.g., interval graphs and circular-arc graphs. We continue the study of these graph classes by considering coloring, clique, and isomorphism problems on H-graphs. We show that for any fixed H conta...

An isomorphism between two graphs is a bijection between their vertices that preserves the edges. We consider the problem of determining whether two finite undirected weighted graphs are isomorphic, and finding an isomorphism relating them if the answer is positive. In this paper we introduce effective probabilistic linear programming (LP) heuristics to solve the graph isomorphism problem. We m...