2006•Unpublished venueRequires access
On the total domination number of trees
Hou Xin-min
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Abstract
For a given connected graph G of order n,a set S of vertices of G is a total dominating set,if every vertex of V(G) is adjacent to some vertex in S.The total domination number of G,denoted by γ_t(G),is the minimum cardinality of a total dominating set of G.We prove that,if T is a tree of order n1 and T≠K_1,n-1,then γ_t(T)≤min{2n3,n-l,n2+l-1}, where l is the number of leaves of T.