In this paper we study the problem of finding the minimum cycle mean in the weighted directed graph. The computational aspect of some algorithms for solving this problem is discussed and two algorithms for minimum cycle mean finding in the weighted directed graph are proposed.

An (edge-)weighted graph is a graph in which each edge e is assigned a nonnegative real number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges, and an optimal cycle is one of maximum weight. The weighted degree w(v) of a vertex v is the sum of the weights of the edges incident with v. The following weighted analogue (and generalization) of a well-known...

The Minimum Weighted Vertex Cover (MWVC) problem is a classic graph optimization NP complete problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the minimum weighted vertex cover problem is to find a vertex set S V whose total weight is minimum subject to every edge of G has at least one end point in S. In this paper an effective algorithm, called Sup...

With the development of industrialization rapidly, vehicles have become an important part of people’s life. However, transportation system is becoming more and more complicated. The core problem of the complicated transportation system is how to avoid hotspots. In this paper, we present a graph model based on a multi-dimension weighted graph for path planning with avoiding hotspots. Firstly, we...

A weighted graph is one in which every edge e is assigned a nonnegative number, called the weight of e. The weight of a graph is defined as the sum of the weights of its edges. In 2-edge-colored complete graph, by using Ramsey-type theorems, we obtain the existence of monochromatic subgraph which have many edges compared with its order. In this paper, we extend the concept of Ramsey problem to ...

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...

A weighted graph is a graph provided with an edge-weighting function w from the edge set to nonnegative real numbers. Bondy and Fan [Annals of Discrete Math. 41 (1989), 53– 69] began the study on the existence of heavy cycles in weighted graphs. Though several results with Dirac-type degree condition can be generalized to Ore-type one in unweighted graphs, it is shown in [Bondy et al., Discuss....

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...