Abstract In this paper the class of Brauer graph algebras is proved to be closed under derived equivalence. For that we use rank maximal torus identity component $$Out^0(A)$$ O u t 0 ( A )</mml:m...

We define and discuss the utility of two equivalence graph classes over which a spectral projector-based graph Fourier transform is equivalent: isomorphic equivalence classes and Jordan equivalence classes. Isomorphic equivalence classes show that the transform is equivalent up to a permutation on the node labels. Jordan equivalence classes permit identical transforms over graphs of nonidentica...

This paper explores the effect of various graphical constructions upon the associated graph C∗-algebras. The graphical constructions in question arise naturally in the study of flow equivalence for topological Markov chains. We prove that outsplittings give rise to isomorphic graph algebras, and in-splittings give rise to strongly Morita equivalent C∗-algebras. We generalise the notion of a del...

Checking that a given finite state program satisfies a linear temporal logic property is suffering in many cases from a severe space and time explosion. One way to cope with this is to reduce the state graph used for model checking. We define an equivalence relation between infinite sequences, based on infinite traces such that for each equivalence class, either all or none of the sequences sat...

Synchronising Graphs is a system of parallel graph transformation designed for modeling process interaction in a network environment. We propose a theory of context-free synchronising graphs and a novel notion of bisimulation equivalence which is shown to be a congruence with respect to graph composition and node restriction. We use this notion of equivalence to study some sample network applic...

Graph transformation systems (GTS) provide an important theory for numerous applications. With the growing number of GTSbased applications the comparison of operational equivalence of two GTS becomes an important area of research. This work introduces a notion of operational equivalence for graph transformation systems. The embedding of GTS in constraint handling rules (CHR) provides the basis ...

a emph{signed graph} (or, in short, emph{sigraph}) $s=(s^u,sigma)$ consists of an underlying graph $s^u :=g=(v,e)$ and a function $sigma:e(s^u)longrightarrow {+,-}$, called the signature of $s$. a emph{marking} of $s$ is a function $mu:v(s)longrightarrow {+,-}$. the emph{canonical marking} of a signed graph $s$, denoted $mu_sigma$, is given as $$mu_sigma(v) := prod_{vwin e(s)}sigma(vw).$$the li...

A knot diagram has an associated looped interlacement graph, obtained from the intersection graph of the Gauss diagram by attaching loops to the vertices that correspond to negative crossings. This construction suggests an extension of the Kauffman bracket to an invariant of looped graphs, and an extension of Reidemeister equivalence to an equivalence relation on looped graphs. The graph bracke...

An equivalence graph is a vertex disjoint union of complete graphs. For a graph G, let eq(G) be the irdnimum number of equivalence subgraphs of G needed to cover all edges of G. Similarly, let cc(G) be the minimum number of complete subgraphs of G needed to cover all its edges. Let H be a graph on n vertices with ma,'dmal degree _~d (and minimal degree --~ 1), and let G=I~ be its complement. We...

An equivalence graph is a disjoint union of cliques, and the equivalence number eq(G) of a graph G is the minimum number of equivalence subgraphs needed to cover the edges of G. We consider the equivalence number of a line graph, giving improved upper and lower bounds: 1 3 log2 log2 χ(G) < eq(L(G)) ≤ 2 log2 log2 χ(G) + 2. This disproves a recent conjecture that eq(L(G)) is at most three for tri...