Triple connected eternal domination in graphs
Künye
Mahadevan, G., Ponnuchamy, T. & Avadayappan, S. (2021). Triple connected eternal domination in graphs. TWMS Journal of Applied and Engineering Mathematics, 11(SI), 88-95.Özet
The concept of Triple connected domination number was introduced by G. Mahadevan et. al., in [10]. The concept of eternal domination in graphs was introduced by W. Goddard., et. al., in [3]. The dominating set S0(? V (G)) of the graph G is said to be an eternal dominating set, if for any sequence v1, v2, v3, . . . vk of vertices, there exists a sequence of vertices u1, u2, u3, . . . uk with ui ? Si?1 and ui equal to or adjacent to vi, such that each set Si = Si?1?{ui}?{vi} is dominating set in G. The minimum cardinality taken over the eternal dominating sets in G is called the eternal domination number of G and it is denoted by ??(G). In this paper we introduce another new concept Triple connected eternal domination in graph. The eternal dominating set S0(? V (G)) of the graph G is said to be a triple connected eternal dominating set, if each dominating set Si is triple connected. The minimum cardinality taken over the triple connected eternal dominating sets in G is called the triple connected eternal domination number of G and it is denoted by ?tc,?(G). We investigate this number for some standard graphs and obtain many results with other graph theoretical parameters.
Cilt
11Sayı
SIBağlantı
http://belgelik.isikun.edu.tr/xmlui/handle/iubelgelik/3024http://jaem.isikun.edu.tr/web/index.php/archive/109-vol11-special-issue/637
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