Secure domination and secure total domination in graphs

2008 ◽  
Vol 28 (2) ◽  
pp. 267 ◽  
Author(s):  
William F. Klostermeyer ◽  
Christina M. Mynhardt
Keyword(s):  
Total Domination ◽  
Domination In Graphs ◽  
Secure Domination

Efficient Secure Domination in Graphs

2015 ◽  
Vol 5 (2) ◽  
pp. 59 ◽  
Author(s):  
P. Roushini Leely Pushpam ◽  
Suseendran Chitra
Keyword(s):  
Domination In Graphs ◽  
Secure Domination

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].

A note on the complexity of locating-total domination in graphs

2019 ◽  
Vol 799 ◽  
pp. 32-39
Author(s):  
Hadi Rahbani ◽  
Nader Jafari Rad ◽  
Mohammad-Reza Sadeghi
Keyword(s):  
Total Domination ◽  
Domination In Graphs

scholarly journals On matching and total domination in graphs

2008 ◽  
Vol 308 (11) ◽  
pp. 2313-2318 ◽  
Author(s):  
Michael A. Henning ◽  
Liying Kang ◽  
Erfang Shan ◽  
Anders Yeo
Keyword(s):  
Total Domination ◽  
Domination In 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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