Graph Searches and Their End Vertices

Competitive graph searches

We exemplify an optimisation criteria for divide-and-conquer algorithms with a technique called generic competitive graph search. The technique is then applied to solve two problems arising from biocomputing, so-called Common Connected Components and Cograph Sandwich. The first problem can be defined as follows: given two graphs on the same set of n vertices, find the coarsest partition of the ...

A measure of similarity between graph vertices

Abstract. We introduce a concept of similarity between vertices of directed graphs. Let GA and GB be two directed graphs with respectively nA and nB vertices. We define a nB × nA similarity matrix S whose real entry sij expresses how similar vertex j (in GA) is to vertex i (in GB) : we say that sij is their similarity score. The similarity matrix can be obtained as the limit of the normalized e...

The Forest Metrics for Graph Vertices

We propose a new graph metric and study its properties. In contrast to the standard distance in connected graphs [5], it takes into account all paths between vertices. Formally, it is defined as d(i, j) = qii+qjj−qij−qji [11], where qij is the (i, j)-entry of the relative forest accessibility matrix Q(ε) = (I + εL)−1, L is the Laplacian matrix of the (weighted) (multi)graph, and ε is a positive...

A minimum broadcast graph on 26 vertices

Broadcasting is the process of information dissemination in a communication network in which a message, originated by one member, is transmitted to all members of the network. A broadcast graph is a graph which permits broadcasting from any originator in minimum time. The broadcast function B(n) is the minimum number of edges in any broadcast graph on n vertices. In this paper, we construct a b...

Inverse scattering problem for quantum graph vertices