As a generalization of connected domination in a graph G we consider domination by sets having at most k components. The order γ _c^k (G) of such a smallest set we relate to γ _c(G), the order of a smallest connected dominating set. For a tree T we give bounds on γ _c^k (T) in terms of minimum valency and diameter. For trees the inequality γ _c^k (T)≤ n-k-1 is known to hold, we determine the class of trees, for which equality holds.

Source : oai:HAL:hal-00961101v1

Volume: Vol. 8

Published on: January 1, 2006

Submitted on: March 26, 2015

Keywords: tree,connected domination,domination,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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