On minus total domination of directed graphs
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
A three-valued function f defined on the vertices of a di- graph D = (V,A), f : V → {−1, 0,+1} is a minus total dominating function(MTDF) if f(N−(v)) ≥ 1 for each vertex v ∈ V . The minus total domination number of a digraph D equals the minimum weight of an MTDF of D. In this paper, we discuss some properties of the minus total domination number and obtain a few lower bounds of the minus total domination number on a digraph D.
Abstract
A three-valued function f defined on the vertices of a di- graph D = (V,A), f : V → {−1, 0,+1} is a minus total dominating function(MTDF) if f(N−(v)) ≥ 1 for each vertex v ∈ V . The minus total domination number of a digraph D equals the minimum weight of an MTDF of D. In this paper, we discuss some properties of the minus total domination number and obtain a few lower bounds of the minus total domination number on a digraph D.
참고문헌 (11)
- J. A. Bondy, "Graph Theory with Application" (1976), Elsevier
- L. Harris, "The algorithmic complexity of certain functional variations of total domination in graphs", Australas. J. Combin, 29, pp.143~156 (2004)
- T. W. Haynes, "Marcel Dekker" (1998), Marcel Dekker
- J. Huang, "The total domination and total bondage numbers of extended de Bruijn and Kautz digraphs", Comput. Math. Appl, 53(8), pp.1206~1213 (2007)
- L. Y. Kang, "Total minus domination in k-partite graphs", Discrete Math, 306(15), pp.1771~1775 (2006)
- C. M. Lee, "Signed and minus total domination on subclasses of bipartite graphs", Ars Combin, 100, pp.129~149 (2011)
- E. F. Shan, "Remarks on the minus (signed) total domination in graphs", Discrete Math, 308(15), pp.3373~3380 (2008)
- S. M. Sheikholeslami, "Signed total domination numbers of directed graphs", Util. Math, 85, pp.273~279 (2011)
- G. Szekeres, "An inequality for the chromatic number of a graph", J. Combinatorial Theory, 4, pp.1~3 (1968)
- H. M. Xing, "Minus total domination in graphs", Czechoslovak Math. J, 59(4), pp.861~870 (2009)
- H. Yan, "Upper minus total domination in small-degree regular graphs", Discrete Math, 307(21), pp.2453~2463 (2007)