We study the parameterized complexity of the graph isomorphism problem when parameterized by width parameters related to tree decompositions. We apply the following technique to obtain fixed-parameter tractability for such parameters. We first compute an isomorphism invariant set of potential bags for a decomposition and then apply a restricted version of the Weisfeiler-Lehman algorithm to solv...

We compute the monoid V (LK(E)) of isomorphism classes of finitely generated projective modules over certain graph algebras LK(E), and we show that this monoid satisfies the refinement property and separative cancellation. We also show that there is a natural isomorphism between the lattice of graded ideals of LK(E) and the lattice of order-ideals of V (LK(E)). When K is the field C of complex ...

The paper contains a construction of a universal countable graph, different from the Rado graph, such that for any of its vertices both the neighbourhood and the non-neighbourhood induce subgraphs isomorphic to the whole graph. This solves an open problem proposed by A. Bonato; see Problem 20 in [5]. We supply a construction of several non-isomorphic graphs with the property, and consider tourn...

In this work, an attempt has been made to represent and simulate fingerprint pattern analysis mathematically using graph isomorphism, dominance pebbling. The idea of categorizing by locating the ridge characteristics attempted be implemented in work. An image is used as input for mathematical modelling simulation. For simulation a fingerprint, we define two techniques. first technique, Algorith...

Graphs are a powerful concept useful for various tasks in science and engineering. In applications such as pattern recognition and information retrieval, object similarity is an important issue. If graphs are used for object representation, then the problem of determining the similarity of objects turns into the problem of graph matching. Some of the most common graph matching paradigms include...

An approach for subgraph isomorphism computation of parameter-ized graphs will be presented. Parameterized graphs (short: p-graphs) are extensions of undirected graphs by parameter vectors at the nodes and edges. We will deene p-graphs and basic concepts of subgraph isomorphism computation for p-graphs. A bottom-up algorithm for p-subgraph isomorphism computation according to a given search gra...

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 present a novel graph kernel framework inspired the by the Weisfeiler-Lehman (WL) isomorphism tests. Any WL test comprises a relabelling phase of the nodes based on test-specific information extracted from the graph, for example the set of neighbours of a node. We defined a novel relabelling and derived two kernels of the framework from it. The novel kernels are very fast to co...

Several cryptographic methods have been developed based on the difficulty to determine the set of solutions of a polynomial system over a given field. We build a polynomial ideal whose algebraic set is related to the set of isomorphisms between two graphs. The problem isomorphism, posed in the context of Graph Theory, has been extensively used in zero knowledge authentication protocols. Thus, a...