Partitioned Graphs and Domination Related Parameters
نویسنده
چکیده
Let G be a graph of order n ≥ 2 and n1, n2, .., nk be integers such that 1 ≤ n1 ≤ n2 ≤ .. ≤ nk and n1 + n2 + .. + nk = n. Let for i = 1, .., k: Ai ⊆ Kni where Km is the set of all pairwise non-isomorphic graphs of order m, m = 1, 2, ... In this paper we study when for a domination related parameter μ (such as domination number, independent domination number and acyclic domination number) is fulfilled μ(G) = μ(∪i=1 < Vi, G >) for all vertex partitions {V1, V2, .., Vk}, k ≥ 2, of a vertex set of G such that < Vi, G > is isomorphic to some a member of Ai, i = 1, 2, .., k. In the process several results for acyclic domination vertex critical graphs are presented. Results for independence number of double vertex graphs are obtained.
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