scholarly journals Bounds on the inverse signed total domination numbers in graphs

2016 ◽  
Vol 36 (2) ◽  
pp. 145
Author(s):  
M. Atapour ◽  
S. Norouzian ◽  
S. M. Sheikholeslami ◽  
L. Volkmann
Keyword(s):  
Total Domination ◽  
Signed Total Domination ◽  
Domination Numbers

On graphs with equal total domination and Grundy total domination numbers

2021 ◽  
Author(s):  
Tanja Dravec ◽  
Marko Jakovac ◽  
Tim Kos ◽  
Tilen Marc
Keyword(s):  
Total Domination ◽  
Domination Numbers

scholarly journals On equality in an upper bound for the restrained and total domination numbers of a graph

2007 ◽  
Vol 307 (22) ◽  
pp. 2845-2852 ◽  
Author(s):  
Peter Dankelmann ◽  
David Day ◽  
Johannes H. Hattingh ◽  
Michael A. Henning ◽  
Lisa R. Markus ◽  
...  
Keyword(s):  
Upper Bound ◽  
Total Domination ◽  
Domination Numbers

scholarly journals Hop Domination in Graphs-II

2015 ◽  
Vol 23 (2) ◽  
pp. 187-199
Author(s):  
C. Natarajan ◽  
S.K. Ayyaswamy
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Total Domination ◽  
Minimum Cardinality ◽  
Unicyclic Graphs ◽  
The Family ◽  
Independent Domination ◽  
Domination In Graphs ◽  
Domination Numbers

Abstract Let G = (V;E) be a graph. A set S ⊂ V (G) is a hop dominating set of G if for every v ∈ V - S, there exists u ∈ S such that d(u; v) = 2. The minimum cardinality of a hop dominating set of G is called a hop domination number of G and is denoted by γh(G). In this paper we characterize the family of trees and unicyclic graphs for which γh(G) = γt(G) and γh(G) = γc(G) where γt(G) and γc(G) are the total domination and connected domination numbers of G respectively. We then present the strong equality of hop domination and hop independent domination numbers for trees. Hop domination numbers of shadow graph and mycielskian graph of graph are also discussed.

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].

Some Results on the Domination Number of a Zero-divisor Graph

2014 ◽  
Vol 57 (3) ◽  
pp. 573-578 ◽  
Author(s):  
Sima Kiani ◽  
Hamid Reza Maimani ◽  
Reza Nikandish
Keyword(s):  
Noetherian Ring ◽  
Zero Divisor ◽  
Domination Number ◽  
Total Domination ◽  
Ore Extension ◽  
Commutative Noetherian Ring ◽  
Zero Divisor Graph ◽  
Domination Numbers

AbstractIn this paper, we investigate the domination, total domination, and semi-total domination numbers of a zero-divisor graph of a commutative Noetherian ring. Also, some relations between the domination numbers of Γ(R/I) and Γ1(R), and the domination numbers of Γ(R) and Γ(R[x, α, δ]), where R[x, α, δ] is the Ore extension of R, are studied.

Effect of vertex-removal on game total domination numbers

2019 ◽  
Vol 13 (07) ◽  
pp. 2050129
Author(s):  
Karnchana Charoensitthichai ◽  
Chalermpong Worawannotai
Keyword(s):  
Domination Number ◽  
Total Domination ◽  
Total Domination Number ◽  
Connected Graphs ◽  
Isolated Vertex ◽  
Vertex Removal ◽  
Total Domination Game ◽  
Domination Game ◽  
Domination Numbers

The total domination game is played on a graph [Formula: see text] by two players, named Dominator and Staller. They alternately select vertices of [Formula: see text]; each chosen vertex totally dominates its neighbors. In this game, each chosen vertex must totally dominates at least one new vertex not totally dominated before. The game ends when all vertices in [Formula: see text] are totally dominated. Dominator’s goal is to finish the game as soon as possible, and Staller’s goal is to prolong it as much as possible. The game total domination number is the number of chosen vertices when both players play optimally, denoted by [Formula: see text] when Dominator starts the game and denoted by [Formula: see text] when Staller starts the game. In this paper, we show that for any graph [Formula: see text] and a vertex [Formula: see text], where [Formula: see text] has no isolated vertex, we have [Formula: see text] and [Formula: see text]. Moreover, all such differences can be realized by some connected graphs.

Global signed total domination in graphs

2011 ◽  
Vol 79 (1-2) ◽  
pp. 7-22 ◽  
Author(s):  
MARYAM ATAPOUR ◽  
SEYED MAHMOUD SHEIKHOLESLAMI ◽  
ABDOLLAH KHODKAR
Keyword(s):  
Total Domination ◽  
Signed Total Domination ◽  
Domination In Graphs
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