The independence equivalence class of a graph $G$ is the set graphs that have same polynomial as $G$. Beaton, Brown and Cameron (arXiv:1810.05317) found classes even cycles, raised problem finding odd cycles. completely solved in this paper.

The main concept of this classification is that graphs belonging to the same equivalence class have similar topological properties. Graphs are called homotopy equivalent if one of them can be converted to the other one by contractible transformations. A basic representative and complexity of a homotopy equivalence class are defined and investigated. Finding a basic representative within a homot...

Equivalence checking is a common problem in formal software design. It is the process of determining whether two systems are equivalent to each other according to some mathematically defined notion of equivalence. In this paper to improve efficiency we present a procedure, based on heuristic searches, for checking the well-know simulation relation defined by Milner. We use heuristic mechanisms ...

Linear time solv-able optimization problems on certain structured graph families, extended abstract. On the xed parameter complexity of graph enumeration problems deenable in monadic second order logic. in preparartion, 1998. 35 the rst case there is no other vertex z of L such that w and z occur in the same equivalence class of R red , or else z and w are adjacent to both u and v, a contradict...

An abstract of the thesis of Yan Chen for the Master of Science in Computer Science presented July 8, 2008. Title: Equivalence Checking for High-Level Synthesis Flow High-level synthesis provides a promising solution to design complicated circuits, but the lack of designers’ confidence in correctness of synthesis tools prevents the wide acceptance in engineering practice. I develop an equivalen...

We study the isomorphism problem of two “natural” algebraic structures – F-algebras and cubic forms. We prove that the F-algebra isomorphism problem reduces in polynomial time to the cubic forms equivalence problem. This answers a question asked in [AS05]. For finite fields of the form 3 6 |(#F − 1), this result implies that the two problems are infact equivalent. This result also has the follo...

The paper presents ALASKA, a multi-layered platform enabling to perform ontological conjunctive query answering (OCQA) over heterogeneously-stored knowledge bases in a generic, logic-based manner. While this problem knows today a renewed interest in knowledge-based systems with the semantic equivalence of different languages widely studied, from a practical view point this equivalence has been ...

In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two isotopy invariants: augmentation number via point-counting over finite field, for variety of Chekanov-Eliashberg differential graded algebra, ruling polynomial combinatorics decompositions front projection.

We give a decomposition formula of the zeta function of a regular covering of a graph G with respect to equivalence classes of prime, reduced cycles of G. Furthermore, we give a decomposition formula of the zeta function of a g-cyclic -cover of a symmetric digraph D with respect to equivalence classes of prime cycles of D, for any 0nite group and g∈ . c © 2002 Elsevier Science B.V. All rights r...

We define a distance between energy forms on graph-like metric measure space and suitable discrete weighted graph using the concept of quasi-unitary equivalence. apply this result to graphs, manifolds (e.g. small neighbourhood an embedded graph) or pcf self-similar fractals as spaces with associated canonical Laplacians, e.g., Kirchhoff Laplacian resp. (Neumann) manifold (with boundary), expres...