Nodes in a dominance graph represent faults of a circuit. A directed edge from node fi to node fj means that fault fj dominates fi. The equivalence of faults fi and fj is indicated by the presence of simultaneous edges fi ! fj and fj ! fi. When local dominance and equivalence relations are included in this graph, its transitive closure provides the collapsed fault sets. Pre-collapsed fault sets...

An end of a graph G is an equivalence class rays, where two rays are equivalent if there infinitely many vertex-disjoint paths between them in G. The degree the maximum cardinality collection pairwise disjoint this class.

Originating from spectral graph theory, cospectrality is a powerful generalization of exchange symmetry and can be applied to all real-valued symmetric matrices. Two vertices an undirected with real edge weights are cospectral iff the underlying weighted adjacency matrix $M$ fulfills $[M^k]_{u,u} = [M^k]_{v,v}$ for non-negative integer $k$, as result any eigenvector $\phi$ has (or, in presence ...

Linear-width is a widely recognized and highly valued graph width parameter. The concepts of linear tangle obstacle are dual linear-width. In this concise paper, we present an alternative proof the equivalence between obstacle.

We prove that for every positive integer k, there exists an mso1-transduction that given a graph of linear cliquewidth at most k outputs, nondeterministically, some clique decomposition of the graph of width bounded by a function of k. A direct corollary of this result is the equivalence of the notions of cmso1-definability and recognizability on graphs of bounded linear cliquewidth.

A method for improving the efficiency of graph isomorphism testing is presented. The method uses the structure of the graph colored by vertex hash codes as a means of partitioning vertices into equivalence classes, which in turn reduces the combinatorial burden of isomorphism testing. Unrolling the graph into a tree at each vertex allows structurally different regular graphs to be discriminated...

It is shown that Poincare* duality groups which satisfy the maximal condition on centralisers have a canonical decomposition as the fundamental group of a finite graph of groups in which the edge groups are polycyclic-by-finite. The results give useful information only when there are large polycyclic subgroups. Since 3-manifolds groups satisfy Max-c, the results provide a purely grouptheoretic ...

In a previous paper we have suggested a graph-theoretic approach to the key equivalence problem. This approach is limited because, to work, it must be supervised. Here we alleviate this requirement by constraining potential solutions to the overall problem while they are generated by the graph-theoretic model already mentioned. This is equivalent to solving an implicit constrained optimisation ...