This paper studies Hennessy Milner classes classes of Kripke models where modal logical equivalence coincides with bisimulation Concepts associated with these classes in the literature Goldblatt Visser are studied and compared and the structure of the collection of maximal Hennessy Milner classes is investigated how many are there what is their intersection The insights into these classes are a...

The Θ-graph Θ(G) of a partial cube G is the intersection graph of the equivalence classes of the Djoković-Winkler relation. Θ-graphs that are 2-connected, trees, or complete graphs are characterized. In particular, Θ(G) is complete if and only if G can be obtained from K1 by a sequence of (newly introduced) dense expansions. Θ-graphs are also compared with familiar concepts of crossing graphs a...

Acyclic digraphs (ADGs) are widely used to describe dependences among variables in multivariate distributions. In particular, the likelihood functions of ADG models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building Bayesian networks for expert systems. There may, however, be many ADGs that determine the same dep...

The input to the Graph Clustering Problem consists of a sequence of integers m 1 ; :::; m t and a sequence of P t i=1 m i graphs. The question is whether the equivalence classes, under the graph isomorphism relation, of the input graphs have sizes which match the input sequence of integers. In this note we show that this problem has a (perfect) zero-knowledge interactive proof system.

In this paper first we introduce the notion of weak $Gamma$-(semi)hypergroups, next some classes of equivalence relations which are called good regular and strongly good regular relations are defined.  Then we investigate some properties of this kind of relations on weak $Gamma$-(semi)hypergroups.

We introduce and study the problem MUTUAL PLANAR DUALITY, which asks for two planar graphs G1 and G2 whether G1 can be embedded such that its dual is isomorphic to G2. Our algorithmic main result is an NP-completeness proof for the general case and a linear-time algorithm for biconnected graphs. To shed light onto the combinatorial structure of the duals of a planar graph, we consider the commo...

The main aim of this study is to characterize new classes of multicone graphs which are determined by their signless Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let C and K w denote the Clebsch graph and a complete graph on w vertices, respectively. In this paper, we show that the multicone graphs K w ▽C are determined by their signless ...

In this paper, W-graph, called the notion of graphs on Wajsberg algebras, is introduced such that vertices graph are elements algebra and edges association two vertices. addition to this, commutative W-graphs also symmetric graphs. Moreover, a equivalence classes constructed. Meanwhile, new definitions as complement annihilator ∆-connection operator algebras presented. Lemmas theorems these not...

In this paper we investigate various properties of equivalence classes of fuzzy equivalence relations over a complete residuated lattice. We give certain characterizations of fuzzy semipartitions and fuzzy partitions over a complete residuated lattice, as well as over a linearly ordered complete Heyting algebra. In the latter case, for a fuzzy equivalence relation over a linearly ordered comple...