In honor of Professor Peter Slater's work on paired domination, we introduce a relaxed version of paired domination, namely semipaired domination. Let G be a graph with vertex set V and no isolated vertices. A subset S ⊆ V is a semipaired dominating set of G if every vertex in V \ S is adjacent to a vertex in S and S can be partitioned into two element subsets such that the vertices in each subset are at most distance two apart. The semipaired domination number γPr2(G) is the minimum cardinality of a semipaired dominating set of G. In this paper, we study the semipaired domination versus other domination parameters. For example, we show that γ(G) ≤ γPr2(G) ≤ 2γ(G) and 2/3γt(G) ≤ γPr2(T) ≤ γ 4/3γt(G), where γ(G) and γt(G) denote the domination and total domination numbers of G. We characterize the trees G for which γPr2(G) = 2γ(G).
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-11601 |
| Date | 01 February 2018 |
| Creators | Haynes, Teresa W., Henning, Michael A. |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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