We propose a dynamic slicing algorithm to compute the slice of concurrent aspect-oriented programs. We use a dependence based intermediate program representation called Concurrent Aspect-oriented System Dependence Graph (CASDG) to represent a concurrent aspect-oriented program. The CASDG of an aspect-oriented program consists of a system dependence graph (SDG) for the non-aspect code, a group o...

The Reserved Graph Grammar (RGG) is a general graph grammar Jormalism that expresses a wide range oj visual languages, This paper presents an extension to RGG with the capability oj spatial specification, Graph transJormation satisfying the spatial specification can be performed in the process oj parsing. The RGG with spatial specification can be applied to various types oj applications, The pa...

An oriented walk double covering of a graph G is a set of oriented closed walks which, traversed successively, combined will have traced each edge of G once in each direction. A bidirectional double tracing of a graph G is an oriented walk double covering which consists of a single closed walk. A retracting in a closed walk is the immediate succession of an edge by its inverse. Every graph with...

For a given hypergraph, an orientation can be assigned to the vertex-edge incidences. This orientation is used to define the adjacency and Laplacian matrices. Continuing the study of these matrices associated to an oriented hypergraph, several related structures are investigated including: the incidence dual, the intersection graph (line graph), and the 2-section. The intersection graph is show...

Grötschel, Thomassen, and Wakabayashi (Hypotraceable digraphs, J. Graph Theory 4 (1980) 377-381) constructed an infinite family of hypotraceable oriented graphs, the smallest of which has order 13. We show that the smallest hypotraceable oriented graph has 8 vertices and 15 arcs. We also show that there exist hypotraceable oriented graphs of order n for every n ≥ 8, except possibly for n = 9, 1...

The relationship between the generalised computational model of Term Graph Rewriting Systems (TGRS) and Object-Oriented Programming (OOP) is explored and exploited by extending the TGRS model with records where access to parameters is done by naming rather than position. Records are then used as the basis for expressing object-oriented techniques such as object encapsulation and (various forms ...

Operators for geographical databases can be classified into two categories: thematic-oriented operators and network-oriented operators. Thematic-oriented operators are based on geometric representations (e.g., intersection, inclusion, adjacency). Network-oriented operators are based on graph manipulations whatever the geometric representation is (e.g., a transitive closure of a graph). In this ...

A digraph is k-traceable if its order is at least k and each of its subdigraphs of order k is traceable. The Traceability Conjecture (TC) states that for k > 2 every k-traceable oriented graph of order at least 2k − 1 is traceable. It has been shown that for 2 6 k 6 6, every k-traceable oriented graph is traceable. We develop an iterative procedure to extend previous results regarding the TC. I...

The exchange graph of a quiver is the graph of mutation-equivalent quivers whose edges correspond to mutations. The exchange graph admits a natural acyclic orientation called the oriented exchange graph. Building on work of Iyama, Reiten, Thomas, and Todorov, we show that this directed graph is a semidistributive lattice by using the isomorphism to the lattice of functorially finite torsion cla...

In this paper we study oriented bipartite graphs. In particular, several characterizations of bitournaments are obtained. We introduce the concept of odd-even graphs and show that any (oriented) bipartite graph can be represented by some (oriented) odd-even graph. We show that the famous Goldbach’s conjecture is equivalent to the connectedness of certain odd-even graphs.