منابع مشابه
Average distance in weighted graphs
Let G be a given connected graph on n vertices. Suppose N facilities are located in the vertices of the graph. We consider the expected distance between two randomly chosen facilities. This is modelled by the following definition: Let G be a connected graph and let each vertex have weight c(v). The average distance of G with respect to c is defined as µ c (G) = N 2 −1 {u,v}⊆V (G) d G (u, v), wh...
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For a graph G where the vertices are coloured, the coloured distance of G is defined as the sum of the distances between all unordered pairs of vertices having different colours. Then for a fixed supply s of colours, ds(G) is defined as the minimum coloured distance over all colourings with s. This generalizes the concepts of median and average distance. In this paper we explore bounds on this ...
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Let G be a connected finite graph. The average distance μ(G) of G is the average of the distances between all pairs of vertices of G. For a positive integer k a k-packing of G is a subset S of the vertex set of G such that the distance between any two vertices in S is greater than k. The k-packing number βk(G) of G is the maximum cardinality of a k-packing of G. We prove upper bounds on the ave...
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Average distance is an important parameter for measuring the communication cost of computer networks. A popular approach for its computation is to first partition the edge set of a network into convex components using the transitive closure of the Djoković-Winkler’s relation and then to compute the average distance from the respective invariants of the components. In this paper we refine this i...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.02.010