Graphs with equal domination and 2-distance domination numbers

2011 ◽  
Vol 31 (2) ◽  
pp. 375
Author(s):  
Joanna Raczek
Keyword(s):  
Distance Domination ◽  
Domination Numbers

scholarly journals Average distances and distance domination numbers

2009 ◽  
Vol 157 (5) ◽  
pp. 1113-1127 ◽  
Author(s):  
Fang Tian ◽  
Jun-Ming Xu
Keyword(s):  
Distance 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 Rainbow domination numbers on graphs with given radius

2014 ◽  
Vol 166 ◽  
pp. 115-122 ◽  
Author(s):  
Shinya Fujita ◽  
Michitaka Furuya
Keyword(s):  
Rainbow Domination ◽  
Domination Numbers

scholarly journals Distance domination of generalized de Bruijn and Kautz digraphs

2016 ◽  
Vol 12 (2) ◽  
pp. 339-357
Author(s):  
Yanxia Dong ◽  
Erfang Shan ◽  
Xiao Min
Keyword(s):  
Kautz Digraphs ◽  
De Bruijn ◽  
Distance 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.

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