Technical Note—Some Average Distance Results
نویسندگان
چکیده
منابع مشابه
Minimum Average Distance Triangulations
Some of the following problems look similar to the MAD Triangulation problem, but we have not found any deep connections: •Minimum Average Distance Spanning Subgraph in a budgeted version [2] was studied in the context of network design (minimizing average routing time). The problem is NP-complete even with unit weights. •Minimum Average Distance Spanning Tree [1]. NP-completeness is implied by...
متن کاملAverage distance in colored graphs
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 ...
متن کاملAverage distance and vertex-connectivity
The average distance μ(G) of a connected graph G of order n is the average of the distances between all pairs of vertices of G, i.e., μ(G) = ( n 2 )−1∑ {x,y}⊂V (G) dG(x, y), where V (G) denotes the vertex set of G and dG(x, y) is the distance between x and y. We prove that if G is a κ-vertex-connected graph, κ ≥ 3 an odd integer, of order n, then μ(G) ≤ n 2(κ+1) + O(1). Our bound is shown to be...
متن کاملAverage Distance and Independence Number
A sharp upper bound on the average distance of a graph depending on the order and the independence number is given. As a corollary we obtain the maximum average distance of a graph with given order and matching number. All extremal graphs are determined.
متن کاملAverage 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transportation Science
سال: 1991
ISSN: 0041-1655,1526-5447
DOI: 10.1287/trsc.25.1.83