Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
A dominating set S in a graph G is a tree dominating set of G if the subgraph induced by S is a tree. The tree domatic number of G is the maximum number of pairwise disjoint tree dominating sets in V(G). First, some exact values of and sharp bounds for the tree domatic number are given. Then, we establish a sharp lower bound for the number of edges in a connected graph of given order and given tree domatic number, and we characterize the extremal graphs. Finally, we show that a tree domatic number of a planar graph is at most 4 and give a characterization of planar graphs with the tree domatic number 3.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
5--11
Opis fizyczny
Bibliogr. 3 poz.
Twórcy
autor
- North China Electric Power University, Department of Mathematics, Beijing 102206, China, gxc_xdm@163.com
Bibliografia
- [1] B. Zelinka, Connected domatic number of a graph, Math. Slovaca 36 (1986), 387-392.
- [2] B.I. Hartnell, D.F. Rall, Connected domatic number in planar graph. Czechoslovak Math. Journal 51 (126) (2001), 173-179.
- [3] X.G. Chen, L. Sun, A. McRae, Tree domination in graphs, Ars Comb. 73 (2004), 193-203.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0008-0001