Several graph problems (e.g., steiner tree, connected domination, hamiltonian path, and isomorphism problem), which can be solved in polynomial time for distance-hereditary graphs, are NP-complete or open for parity graphs. Moreover, the metric characterizations of these two graph classes suggest an excessive gap between them. We introduce a family of classes forming an infinite lattice with re...

Graph isomorphism checking can be used in graph-based model checking to achieve symmetry reduction. Instead of one-to-one comparing the graph representations of states, canonical forms of state graphs can be computed. These canonical forms can be used to store and compare states. However, computing a canonical form for a graph is computationally expensive. Whether computing a canonical represen...

The isomorphism problem is neither known to be NP-complete nor polynomial. Yet it is crucial for managing large conceptual graph sets. In order to speed up the conceptual graph isomorphism test, we associate to graphs a textual code that is invariant under isomorphism: a structural or ltering code. The structural code of a given graph is based on the computation by a structural function of an i...

The graph isomorphism problem can be easily stated: check to see if two graphs that look di erently are actually the same. The problem occupies a rare position in the world of complexity theory, it is clearly in NP but is not known to be in P and it is not known to be NP-complete. Many sub-disciplines of mathematics, such as topology theory and group theory, can be brought to bear on the proble...

Graph isomorphism is an important and widely studied computational problem with a yet unsettled complexity. However, the exact complexity is known for isomorphism of various classes of graphs. Recently, [8] proved that planar isomorphism is complete for log-space. We extend this result further to the classes of graphs which exclude K3,3 or K5 as a minor, and give a log-space algorithm. Our algo...

In the subgraph querying problem, given a query graph and a dataset of graphs, we want to locate which graphs in the dataset contain the query and/or find all its occurrences. Over the years, numerous methods, fragmented in 2 categories, were proposed to tackle the problem. In the first category, methods follow the filter-then-verify (FTV) paradigm where an index is used to filter out graphs th...

The k -dimensional Weisfeiler-Leman procedure ( - WL ), which colors -tuples of vertices in rounds based on the neighborhood structure graph, has proven to be immensely fruitful algorithmic study Graph Isomorphism. More generally, it is fundamental importance understanding and exploiting symmetries graphs various settings. Two are -equivalent if produces same final coloring both graphs. 1 -equi...

We derive strong structural constraints on the automorphism groups of strongly regular (s. r.) graphs, giving a surprisingly strong answer to a decades-old problem, with tantalizing implications to testing isomorphism of s. r. graphs, and raising new combinatorial challenges. S. r. graphs, while not believed to be Graph Isomorphism (GI) complete, have long been recognized as hard cases for GI, ...

In this paper, we show that all fat Hoffman graphs with smallest eigenvalue at least −1−τ , where τ is the golden ratio, can be described by a finite set of fat (−1 − τ)-irreducible Hoffman graphs. In the terminology of Woo and Neumaier, we mean that every fat Hoffman graph with smallest eigenvalue at least −1−τ is anH-line graph, where H is the set of isomorphism classes of maximal fat (−1−τ)-...