for a graph g, let d(g) be the set of all strong orientations of g. the orientationnumber of g is min {d(d) |d belongs to d(g)}, where d(d) denotes the diameterof the digraph d. in this paper, we determine the orientation number for some subgraphs of complete bipartite graphs.

This article establishes that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic.This result is actually an instance of a more general result covering canonical graph decompositions like the modular decomposition and the Tutte decomposition of 2-connected graphs into 3-connected components. As an application, we prove that the set of graphs hav...

Our web user prooles consist of Page Interest Estimators (PIE's) and Web Access Graphs (WAG's). We discuss a non-invasive approach to estimating the user's interest of a web page without directly asking the user. A time and space eecient method is proposed for locating multi-word phrases to enrich the common bag-of-words representation for text documents. PIE's are then learned to predict the u...

One of the most successful techniques for frontal face authentication is based on matching image graphs that represent faces. The local identity information is stored at node graph locations through vectors of multi-scale and multi-orientation Gabor image responses. In this work we present an efficient way to process f¡ontal faces by automatically locating graph nodes at selected crease pointsT...

The Median-Path problem consists of locating a path on a network, minimizing a function of two parameters: accessibility to the path and total cost of the path. Applications of this problem can be found in transportation planning, water resource management and fluid transportation. The Central-Path problem is defined similarly. In this paper, we give a construction on a graph G which produces a...

In this paper, we introduce some new versions based on the locating vectors named indices. particular, Hyper indices, Randić index, and Sambor index. The exact formulae for these indices of well-known families graphs Helm graph are derived. Moreover, determine importance 11 benzenoid hydrocarbons. Furthermore, show that have a reasonable correlation using linear regression with physicochemical ...

Domination in graphs is an emerging area of research at present and it has applications to several fields such as School bus routing, Computer communication networks, Facility location problems, Locating radar stations problem etc. Recently dominating functions in domination theory have received much attention. The new concepts viz., unidominating functions and total unidominating functions hav...

For a graph G that models a facility, various detection devices can be placed at the vertices so as to identify the location of an intruder such as a thief or saboteur. Here we introduce the open neighborhood locating-dominating set problem. We seek a minimum cardinality vertex set S with the property that for each vertex v its open neighborhood N(v) has a unique non-empty intersection with S. ...

We study the problem of locating sensors to detect the failure of any set of radiation sources in a system. For computing illumination data, we suggest the use of radiosity methods. We then consider the problem of optimising sensor placement to unambiguously identify any inactive sources. We show that the problem can be transformed from a numerical to a geometrical domain, relate it to set cove...