In the real world, many phenomena can be naturally modeled as a graph whose nodes represent entities and whose edges represent interactions or relationships between the entities. Past and ongoing research on graphs has developed concepts and theories that may deepen the understanding of the graph data and facilitate solving many problems of practical interest represented by graphs. However, lit...

The research of Boolean index sets of graphs is one of the most important graph theories in the graph theory . Boolean index sets of graphs are to use the vertex sets and the edge sets of graphs to study the characteristics of various graphs and their inherent characteristics through corresponding the mapping function to 2 Z . It’s theory can be applied to information engineering, communication...

The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set. While in combinatorial optimization the point is in developing efficient algorithms and heuristics for solving specified types of problems, the extremal graph theory deals with finding bounds for various graph invariants u...

A reasoning method that proves a predicate logic formula by reducing its graph representation is proposed. Since the method directly reduces a logic formula represented by a graph, it can be understood to self-optimize a graph representation, meaning that it automatically transforms a logic formula into an eecient form equivalent to that acquired by Explanation-Based Learning. By sharing the or...

In this note, I discuss a dual version of the ribbon graph decomposition of the moduli spaces of Riemann surfaces with boundary and marked points, which I introduced in the unpublished preprint [1], and used in [2] to construct open-closed topological conformal field theories. This dual version of the ribbon graph decomposition is a compact orbi-cell complex with a natural weak homotopy equival...

There is general agreement that structural similarity — a match in relational structure — is crucial in analogical processing. However, theories differ in their definitions of structural similarity: in particular, in whether there must be conceptual similarity between the relations in the two domains or whether parallel graph structure is sufficient. In two studies, we demonstrate, first, that ...

Canonical trace model of Hoare and He supports a satisfactory theory of graph properties. We use it to define a technique for the general composition of properties that extends the parallel-by-merge of Unifying Theories of Programming, and apply that to unique decompositions. Applications are provided to the fundamental concepts of acyclicity, reachability and canonicity; and those are used, in...

the fact that the properties of a molecule are tightly connected to its structural  characteristics  is one of the fundamental concepts in chemistry. in this connection,  graph theory has been successfully applied in developing some relationships between topological indices and some thermodynamic properties. so ,  a novel method for computing the new descriptors to construct a quantitative rela...

Let T1, T2 be countable first-order theories, Mi |= Ti, and D any regular ultrafilter on λ ≥ א0. A longstanding open problem of Keisler asks when T2 is more complex than T1, as measured by the fact that for any such λ,D, if the ultrapower (M2)/D realizes all types over sets of size ≤ λ, then so must the ultrapower (M1)/D. In this paper, building on the author’s prior work [11] [12] [13], we sho...

Constraint solvers are key modules in many systems with reasoning capabilities (e.g., automated theorem provers). To incorporate constraint solvers in such systems, the capability of producing conflict sets or explanations of their results is crucial. For expressiveness, constraints are usually built out in unions of theories and constraint solvers in such unions are obtained by modularly combi...