Independence and average distance in graphs
نویسندگان
چکیده
منابع مشابه
Average 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.
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For a set D of positive integers, we define a vertex set S ⊆ V (G) to be D-independent if u, v ∈ S implies the distance d(u, v) 6∈ D. The D-independence number βD(G) is the maximum cardinality of a D-independent set. In particular, the independence number β(G) = β{1}(G). Along with general results we consider, in particular, the odd-independence number βODD(G) where ODD = {1, 3, 5, . . .}.
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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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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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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1997
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(96)00078-9