Fine-grained reductions have established equivalences between many core problems with Õ(n3)-time algorithms on n-node weighted graphs, such as Shortest Cycle, All-Pairs Shortest Paths (APSP), Radius, Replacement Paths, Second Shortest Paths, and so on. These problems also have Õ(mn)-time algorithms on m-edge n-node weighted graphs, and such algorithms have wider applicability. Are these mn boun...

Can a directed graph be completed to a directed line graph? If possible, how many arcs must be added? In this paper we address the above questions characterizing partial directed line (PDL) graphs, i.e., partial subgraph of directed line graphs.We show that for such class of graphs a forbidden configuration criterion and a Krausz’s like theorem are equivalent characterizations. Furthermore, the...

Understanding cattle metabolism and its relationship with milk products is important in bovine breeding. A systemic view could lead to consequences that will result in a better understanding of existing concepts. Topological indices and quantitative characterizations mostly result from the application of graph theory on biological data. In the present work, the enzyme network involved in cattle...

In general the problem of finding a miminum spanning tree for a weighted directed graph is difficult but solvable. There are a lot of differences between problems for directed and undirected graphs, therefore the algorithms for undirected graphs cannot usually be applied to the directed case. In this paper we examine the kind of weights such that the problems are equivalent and a minimum spanni...

This paper proposes an algorithm for buUdmg weighted directed graph,defmes the weighted directed relationship matrix of the graph,an d describes algorithm implementation using this matrix.Based on this algorithm ,an effective way for building an d drawing weighted directed graphs is presented,forming a foundation for visual implementation of the algorithm in the graph theory.

We give laws of large numbers (in the Lp sense) for the total length of the k-nearest neighbours (directed) graph and the j-th nearest neighbour (directed) graph in Rd, d ∈ N, with power-weighted edges. We deduce a law of large numbers for the standard nearest neighbour (undirected) graph. We give the limiting constants, in the case of uniform random points in (0, 1)d, explicitly. Also, we give...

A power digraph, denoted by $G(n,k)$, is a directed graph with $Z_{n}={0,1,..., n-1}$ as the set of vertices and $L={(x,y):x^{k}equiv y~(bmod , n)}$ as the edge set, where $n$ and $k$ are any positive integers. In this paper, the structure of $G(2q+1,k)$, where $q$ is a Sophie Germain prime is investigated. The primality tests for the integers of the form $n=2q+1$ are established in terms of th...

Network design on directed graphs are problems that require to select a minimum cost directed subgraph of a given edge-weighted directed graph, under some constraints. One of the main goals of this proposal is to understand some of the most fundamental network design problems on directed graphs whose exact approximability status remains unclear for a very long time. Directed graphs appear frequ...

In this paper, we tackle the task of graph language learning. We first extend the well-known classes of k-testability and k-testability in the strict sense languages to directed graph languages. Second, we propose a graph automata model for directed acyclic graph languages. This graph automata model is used to propose a grammatical inference algorithm to learn the class of directed acyclic k-te...

In this paper, we propose a new edge-based matching kernel for graphs by using discrete-time quantum walks. To this end, we commence by transforming a graph into a directed line graph. The reasons of using the line graph structure are twofold. First, for a graph, its directed line graph is a dual representation and each vertex of the line graph represents a corresponding edge in the original gr...