On the spanning w-wide diameter of the star graph
Let a and v be any two distinct nodes of an undirected graph G, which is k-connected. A container C(u, v) between a and v is a set of internally disjoint paths {P(1), P(2),..., P(W)} between a and v where 1  = 5. It is known that S(n) is bipartite. In this article, we show that, for any pair of distinct nodes u and v in different partite sets of S(n), there exists an (n - 1)*-container C(u, v) and the (n - 1)-wide distance d((n-1))(u, v) is less than or equal to n!/n-2 + 1. In addition, we also show the existence of a 2*-container C(u, v) and the 2-wide distance d(2)(u, v) is bounded above by nI/2 + 1. (C) 2006 Wiley Periodicals, Inc.
diameter star graphs hamiltonian hamiltonian laceable