Semipaired Domination in Claw-Free Cubic Graphs
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Publication Details
Author list: Henning M.A., Kaemawichanurat P.
Publisher: Springer Tokyo
Publication year: 2018
Volume number: 34
Issue number: 4
Start page: 819
End page: 844
Number of pages: 26
ISSN: 0911-0119
eISSN: 0911-0119
Languages: English-Great Britain (EN-GB)
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Abstract
A subset S of vertices in a graph G is a dominating set if every vertex in V(G) \ S is adjacent to a vertex in S. If the graph G has no isolated vertex, then a semipaired dominating set of G is a dominating set of G with the additional property that the set 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 γpr 2(G) is the minimum cardinality of a semipaired dominating set of G. We show that if G is a claw-free, connected, cubic graph of order n≥ 10 , then γpr2(G)≤25n. © 2018, Springer Japan KK, part of Springer Nature.
Keywords
Claw-free, Cubic, Paired-domination, Semipaired domination number
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