A lot of real world problems can be modeled as traversals on graph, and mining from such traversals has been found useful in several applications. However, previous works considered only traversals on unweighted graph. This paper generalizes this to the case where vertices of graph are given weights to reflect their importance. Under such weight settings, traditional mining algorithms can not b...

Let K(G) be the clique graph of a graph G. A m-weighting of K(G) consists on giving to each m-size subset of its vertices a weight equal to the size of the intersection of the m corresponding cliques of G. The 2weighted clique graph was previously considered by McKee. In this work we obtain a characterization of weighted clique graphs similar to Roberts and Spencer’s characterization for clique...

We consider the problem of placing k identical resources in a graph where each vertex is associated with a nonnegative weight representing the frequency of requests issued by that vertex for the resource. We de ne the cost of a placement as the sum over all vertices of their distances to the closest resource weighted by their weights. The optimal placement is the placement with least cost among...

An extended star is a tree which has only one vertex with degree larger than two. The -center problem in a graph  asks to find a subset  of the vertices of  of cardinality  such that the maximum weighted distances from  to all vertices is minimized. In this paper we consider the -center problem on the unweighted extended stars, and present some properties to find solution.

In traditional edge searching one tries to clean all of the edges in a graph employing the least number of searchers. It is assumed that each edge of the graph initially has a weight equal to one. In this paper we modify the problem and introduce the Weighted Edge Searching Problem by considering graphswith arbitrary positive integerweights assigned to its edges. We give bounds on the weighted ...

In this paper, we study curvature dimension conditions on birth-death processes which correspond to linear graphs, i.e., weighted graphs supported the infinite line or half line. We give a combinatorial characterization of Bakry and Émery’s CD(K,n) condition for prove triviality edge weights every graph Z with non-negative curvature. Moreover, show that decaying not faster than −R2 are stochast...

abstract background: a major problem of the first moments of childbirth, especially in “prolonged labor,” is perinatal asphyxia which necessitates neonatal resuscitation. this study aimed at evaluating the alert line of the partogram in recognizing the need for neonatal resuscitation 20–30 s after delivery. materials and methods: 140 full‑term pregnant women were kept under surveillance through...

We study the set of probability distributions visited by a continuous-time quantum walk on graphs. An edge-weighted graph G is universal mixing if the instantaneous or average probability distribution of the quantum walk on G ranges over all probability distributions on the vertices as the weights are varied over non-negative reals. The graph is uniform mixing if it visits the uniform distribut...