On independent domination parameters of some special families of Halin graph

2019 ◽  
Vol 22 (6) ◽  
pp. 1113-1119
Author(s):  
D. Anandhababu ◽  
M. Priyadharshini ◽  
N. Parvathi
Keyword(s):  
Halin Graph ◽  
Independent Domination

scholarly journals Independent domination in subcubic graphs

2021 ◽  
Author(s):  
A. Akbari ◽  
S. Akbari ◽  
A. Doosthosseini ◽  
Z. Hadizadeh ◽  
Michael A. Henning ◽  
...  
Keyword(s):  
Independent Domination ◽  
Subcubic Graphs

scholarly journals Independence and domination on shogiboard graphs

2017 ◽  
Vol 4 (8) ◽  
pp. 25-37 ◽  
Author(s):  
Doug Chatham
Keyword(s):  
Independence Number ◽  
Domination Number ◽  
The Other ◽  
Independent Domination

Abstract Given a (symmetrically-moving) piece from a chesslike game, such as shogi, and an n×n board, we can form a graph with a vertex for each square and an edge between two vertices if the piece can move from one vertex to the other. We consider two pieces from shogi: the dragon king, which moves like a rook and king from chess, and the dragon horse, which moves like a bishop and rook from chess. We show that the independence number for the dragon kings graph equals the independence number for the queens graph. We show that the (independent) domination number of the dragon kings graph is n − 2 for 4 ≤ n ≤ 6 and n − 3 for n ≥ 7. For the dragon horses graph, we show that the independence number is 2n − 3 for n ≥ 5, the domination number is at most n−1 for n ≥ 4, and the independent domination number is at most n for n ≥ 5.

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.

Independent Domination in Triangle Graphs

2007 ◽  
Vol 28 ◽  
pp. 341-348 ◽  
Author(s):  
Yu.L. Orlovich ◽  
I.E. Zverovich
Keyword(s):  
Independent Domination
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