scholarly journals Upper bounds on the upper signed total domination number of graphs

2009 ◽  
Vol 157 (5) ◽  
pp. 1098-1103 ◽  
Author(s):  
Erfang Shan ◽  
T.C.E. Cheng
Keyword(s):  
Domination Number ◽  
Upper Bounds ◽  
Total Domination ◽  
Total Domination Number ◽  
Signed Total Domination Number ◽  
Signed Total Domination

scholarly journals New bounds on the signed total domination number of graphs

2016 ◽  
Vol 36 (2) ◽  
pp. 467 ◽  
Author(s):  
S.M. Hosseini Moghaddam ◽  
Doost Ali Mojdeh ◽  
Babak Samadi ◽  
Lutz Volkmann
Keyword(s):  
Domination Number ◽  
Total Domination ◽  
Total Domination Number ◽  
Signed Total Domination Number ◽  
Signed Total Domination

scholarly journals Total Transversals and Total Domination in Uniform Hypergraphs

10.37236/3866 ◽  
2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Csilla Bujtás ◽  
Michael Henning ◽  
Zsolt Tuza ◽  
Anders Yeo
Keyword(s):  
Domination Number ◽  
Upper Bounds ◽  
Total Domination ◽  
Total Domination Number ◽  
Uniform Hypergraphs ◽  
Transversal Number ◽  
Edge Size

In 2012, the first three authors established a relationship between the transversal number and the domination number of uniform hypergraphs. In this paper, we establish a relationship between the total transversal number and the total domination number of uniform hypergraphs. We prove tight asymptotic upper bounds on the total transversal number in terms of the number of vertices, the number of edges, and the edge size.

The minus total k-domination numbers in graphs

2021 ◽  
pp. 2150150
Author(s):  
Jonecis Dayap ◽  
Nasrin Dehgardi ◽  
Leila Asgharsharghi ◽  
Seyed Mahmoud Sheikholeslami
Keyword(s):  
Domination Number ◽  
Total Domination ◽  
Total Domination Number ◽  
Sharp Bounds ◽  
Number Formula ◽  
Domination In Graphs ◽  
Dominating Function ◽  
Domination Numbers

For any integer [Formula: see text], a minus total [Formula: see text]-dominating function is a function [Formula: see text] satisfying [Formula: see text] for every [Formula: see text], where [Formula: see text]. The minimum of the values of [Formula: see text], taken over all minus total [Formula: see text]-dominating functions [Formula: see text], is called the minus total [Formula: see text]-domination number and is denoted by [Formula: see text]. In this paper, we initiate the study of minus total [Formula: see text]-domination in graphs, and we present different sharp bounds on [Formula: see text]. In addition, we determine the minus total [Formula: see text]-domination number of some classes of graphs. Some of our results are extensions of known properties of the minus total domination number [Formula: see text].

A note on improved upper bounds on the transversal number of hypergraphs

2019 ◽  
Vol 11 (01) ◽  
pp. 1950004
Author(s):  
Michael A. Henning ◽  
Nader Jafari Rad
Keyword(s):  
Upper Bound ◽  
Dominating Set ◽  
Domination Number ◽  
Minimum Size ◽  
Total Domination ◽  
Total Domination Number ◽  
Minimum Cardinality ◽  
Total Dominating Set ◽  
Isolated Vertex ◽  
Transversal Number

A subset [Formula: see text] of vertices in a hypergraph [Formula: see text] is a transversal if [Formula: see text] has a nonempty intersection with every edge of [Formula: see text]. The transversal number of [Formula: see text] is the minimum size of a transversal in [Formula: see text]. A subset [Formula: see text] of vertices in a graph [Formula: see text] with no isolated vertex, is a total dominating set if every vertex of [Formula: see text] is adjacent to a vertex of [Formula: see text]. The minimum cardinality of a total dominating set in [Formula: see text] is the total domination number of [Formula: see text]. In this paper, we obtain a new (improved) probabilistic upper bound for the transversal number of a hypergraph, and a new (improved) probabilistic upper bound for the total domination number of a graph.

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