629 research outputs found
On a Class of Graphs with Large Total Domination Number
Let and denote the domination number and the total
domination number, respectively, of a graph with no isolated vertices. It
is well-known that . We provide a characterization
of a large family of graphs (including chordal graphs) satisfying , strictly generalizing the results of Henning (2001) and Hou et al.
(2010), and partially answering an open question of Henning (2009).Comment: 9 pages, 4 figure
New bounds on the signed total domination number of graphs
In this paper, we study the signed total domination number in graphs and
present new sharp lower and upper bounds for this parameter. For example by
making use of the classic theorem of Turan, we present a sharp lower bound on
this parameter for graphs with no complete graph of order r+1 as a subgraph.
Also, we prove that n-2(s-s') is an upper bound on the signed total domination
number of any tree of order n with s support vertices and s' support vertives
of degree two. Moreover, we characterize all trees attainig this bound.Comment: This paper contains 11 pages and one figur
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