Average distance and generalised packing in graphs
نویسندگان
چکیده
منابع مشابه
Average distance and generalised packing in graphs
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...
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 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 کاملPacking Chromatic Number of Distance Graphs
The packing chromatic number (G) of a graph G is the smallest integer k such that vertices of G can be partitioned into disjoint classes X1; :::; Xk where vertices in Xi have pairwise distance greater than i. We study the packing chromatic number of in nite distance graphs G(Z; D), i.e. graphs with the set Z of integers as vertex set and in which two distinct vertices i; j 2 Z are adjacent if a...
متن کاملOn Packing Colorings of Distance Graphs
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau...
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: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2010.05.006