We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
The 2-Rainbow Domination of Sierpiński Graphs and Extended Sierpiński Graphs.
- Authors
Liu, Jia-Jie; Chang, Shun-Chieh; Lin, Chiou-Jiun
- Abstract
Let G( V, E) be a connected and undirected graph with n-vertex-set V and m-edge-set E. For each v ∈ V, let N( v) = { u| v ∈ V and( u, v) ∈ E}. For a positive integer k, a k-rainbow dominating function of a graph G is a function f from V( G) to a k-bit Boolean string f( v) = f ( v) f ( v) ... f ( v), i.e., f ( v) ∈ {0, 1}, 1 ≤ i ≤ k, such that for any vertex v with f( v) = 0 we have ⋈ f( u) = 1, for all v ∈ V, where ⋈ f( u) denotes the result of taking bitwise OR operation on f( u), for all u ∈ S. The weight of f is defined as $w(f) = {\sum }_{v\in V}{\sum }^{k}_{i=1} f_{i}(v)$ . The k-rainbow domination number γ ( G) is the minimum weight of a k-rainbow dominating function over all k-rainbow dominating functions of G. The 1-rainbow domination is the same as the ordinary domination. The k-rainbow domination problem is to determine the k-rainbow domination number of a graph G. In this paper, we determine γ ( S( n, m)), γ ( S ( n, m)), and γ ( S ( n, m)), where S( n, m), S ( n, m), and S ( n, m) are Sierpiński graphs and extended Sierpiński graphs.
- Subjects
DOMINATING set; GRAPH theory; PATHS &; cycles in graph theory; GRAPH connectivity; UNDIRECTED graphs
- Publication
Theory of Computing Systems, 2017, Vol 61, Issue 3, p893
- ISSN
1432-4350
- Publication type
Article
- DOI
10.1007/s00224-017-9756-y