Hajj os theorem states that every graph with chromatic number at least k can be obtained from the complete graph K k by a sequence of simple operations such that every intermediate graph also has chromatic number at least k. Here, Hajj os theorem is extended in three slightly diierent ways to colorings and circular colorings of edge-weighted graphs. These extensions shed some new light on the H...

Frequent sub-graph mining entails two significant overheads. The first is concerned with candidate set generation. The second with isomorphism checking. These are also issues with respect to other forms of frequent pattern mining but are exacerbated in the context of frequent sub-graph mining. To reduced the search space, and address these twin overheads, a weighted approach to sub-graph mining...

A k-weighted graph is a directed graph where each vertex has k associated weights. Partitioning such a graph so that each weight is roughly evenly divided into each piece is useful for balancing a parallel task with k distinct components. Such a goal arises in crash simulation, in which there there are 2 components. We present a 2-weighted graph partitioning algorithm, based on the Ham Sandwich...

This thesis describes research work undertaken in the field of graph-based knowledge discovery (or graph mining). The objective of the research is to investigate the benefits that the concept of weighted frequent subgraph mining can offer in the context of the graph model based classification. Weighted subgraphs are graphs where some of the vertexes/edges are considered to be more significant t...

In this paper, we will describe some algorithms and give their complexity as following: (1) The algorithm for finding a dominating set of radius r in a vertex-weighted graph with small number of spanning tress. The complexity of this algorithm for the unicyclic graph is O(m.n). (2) The algorithm for finding an absolute and vertex p-center of a vertex-weighted graph with small number of spanning...

In this paper, we develop the idea to partition the edges of a weighted graph in order to uncover overlapping communities of its nodes. Our approach is based on the construction of different types of weighted line graphs, i.e. graphs whose nodes are the links of the original graph, that encapsulate differently the relations between the edges. Weighted line graphs are argued to provide an altern...