in a graph g = (v,e), a subset s  v is said to be an open packing set if no two vertices of s have a common neighbour in g. the maximum cardinality of an open packing set is called the open packing number and is denoted by rho^o. this paper further studies on this parameter by obtaining some new bounds.

we find recursive formulae for the number of perfect matchings in a graph g by splitting g into subgraphs h and q. we use these formulas to count perfect matching of p hypercube qn. we also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in g, is the graph constructed from by deleting edges with an en...

Solvable Graphs (also known as Reachable Graphs) are types of graphs that any arrangement of a specified number of agents located on the graph’s vertices can be reached from any initial arrangement through agents’ moves along the graph’s edges, while avoiding deadlocks (interceptions). In this paper, the properties of Solvable Graphs are investigated, and a new concept in multi agent moti...

We present some techniques for planning in temporal domains specified with the recent standard languange PDDL2.1. These techniques are implemented in LPG, a fully-automated system that took part in the third International Planning Competition (Toulouse, 2002) showing excellent performance. The planner is based on a stochastic local search method and on a graph-based representation called “Tempo...

The problem of finding a pleasant layout for a given graph is a key challenge in the field of information visualization. For graphs that are biased towards a particular property such as tree-like, star-like, or bipartite, a layout algorithm can produce excellent layouts—if this property is actually detected. Typically, a graph may not be of such a homogeneous shape but is comprised of different...

Triangle counting is an important problem in graph mining. Clustering coefficients of vertices and the transitivity ratio of the graph are two metrics often used in complex network analysis. Furthermore, triangles have been used successfully in several real-world applications. However, exact triangle counting is an expensive computation. In this paper we present the analysis of a practical samp...

We are looking at a model of preferential attachment graphs that can evolve in five different ways. On any given iteration, a single vertex may be connected to the graph, a path may be connected to the graph, an edge may be added to the graph, an edge may be removed from a graph, or a vertex may be removed from a graph, with each option having a given probability of occurring. If a single verte...

The general problem of path planning can be modeled as a traveling salesman problem which assumes that a graph is fully connected. Such a scenario of full connectivity is however not always realistic. One such motivating example for us is the application of path planning for unmanned reconnaissance aerial vehicles (URAVs). URAVs are widely deployed for photography or imagery gathering missions ...

Internet-based social networks are facilities (typically web sites) where people can form online communities, connect to each other and share information. This paper explores the area of applying visual analytics to represent data and underlying relationships in social networks – more specifically, on the Twitter micro-blogging service. Networks of this kind can be treated as graphs, where each...

The process of healthy aging can best be described by plotting the trajectory of health-related variables over time. Unfortunately, graphs including data only from survivors may be misleading because they may confuse patterns of mortality with patterns of change in health. Two approaches for creating graphs that account for death in such situations are 1) to incorporate a category or value for ...