ÐGraphs are a powerful and universal data structure useful in various subfields of science and engineering. In this paper, we propose a new algorithm for subgraph isomorphism detection from a set of a priori known model graphs to an input graph that is given online. The new approach is based on a compact representation of the model graphs that is computed offline. Subgraphs that appear multiple...

In this paper, we propose a heuristic for the graph isomorphism problem that is based on the eigendecomposition of the adjacency matrices. It is well known, that the eigenvalues of the adjacency matrices of isomorphic graphs need to be identical. However, two graphs GA and GB can be isospectral but non-isomorphic. If the graphs possess repeated eigenvalues, which typically correspond to graph s...

The complexity of the graph isomorphism problem for trapezoid graphs has been open over a decade. This paper shows that the problem is GI-complete. More precisely, we show that the graph isomorphism problem is GI-complete for comparability graphs of partially ordered sets with interval dimension 2 and height 3. In contrast, the problem is known to be solvable in polynomial time for comparabilit...

In this lecture, I will present three results related to Strongly Regular Graphs. 1. An algorithm for testing isomorphism of SRGs that runs in time 2 O(√ n log n). 2. A proof that f and g, the dimensions of the eigenspaces, are both at least √ n. The problem of testing isomorphism of graphs is often reduced to the problem of giving each vertex in a graph a unique name. If we have a way of doing...

In this paper we show how isomorphism checking can be used as an effective technique for symmetry reduction in graph-based state spaces, despite the inherent complexity of the isomorphism problem. In particular, we show how one can use element-based graph certificate mappings to help in recognising nonisomorphic graphs. These are mappings that assign to all elements (edges and nodes) of a given...

In this work a convex relaxation of a subgraph isomorphism problem is proposed, which leads to a new lower bound that can provide a proof that a subgraph isomorphism between two graphs can not be found. The bound is based on a semidefinite programming relaxation of a combinatorial optimisation formulation for subgraph isomorphism and is explained in detail. We consider subgraph isomorphism prob...

We study infinite limits of graphs generated by the duplication model for biological networks. We prove that with probability 1, the sole nontrivial connected component of the limits is unique up to isomorphism. We describe certain infinite deterministic graphs which arise naturally from the model. We characterize the isomorphism type and induced subgraph structure of these infinite graphs usin...