Results 291 to 300 of about 128,488 (305)

Double Roman Domination in Digraphs

Bulletin of the Malaysian Mathematical Sciences Society, 2017
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Guoliang Hao, Xiaodan Chen, Lutz Volkmann   +2 more
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INVERSE ROMAN DOMINATION IN GRAPHS

Discrete Mathematics, Algorithms and Applications, 2013
Motivated by the article in Scientific American [7], Michael A Henning and Stephen T Hedetniemi explored the strategy of defending the Roman Empire. Cockayne defined Roman dominating function (RDF) on a Graph G = (V, E) to be a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex
Kumar, M. Kamal, Reddy, L. Sudershan
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Weak Double Roman Domination

Bulletin of the Malaysian Mathematical Sciences Society
The authors introduce a new variant of domination in graphs called weak double Roman domination (WDRD), which generalizes the well-studied concept of double Roman domination (DRD) by relaxing certain constraints. Given a graph \( G = (V, E) \), a WDRD-function is a labeling \( f: V \to \{0,1,2,3\} \) that satisfies the following condition: every vertex
Soltani, S., Ahangar, H. Abdollahzadeh, Chellali, M., Rahbani, H., Sheikholeslami, S. M.   +4 more
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Relations between the Roman k-domination and Roman domination numbers in graphs

Discrete Mathematics, Algorithms and Applications, 2014
Let G = (V, E) be a graph and let k be a positive integer. A Roman k-dominating function ( R k-DF) on G is a function f : V(G) → {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least k vertices v1, v2, …, vk with f(vi) = 2 for i = 1, 2, …, k.
Bouchou, Ahmed, Blidia, Mostafa, Chellali, Mustapha   +2 more
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Roman Domination and Double Roman Domination Numbers of Sierpiński Graphs $$S(K_n,t)$$

Bulletin of the Malaysian Mathematical Sciences Society, 2021
Sierpiński graph \(S_n^t\) can be defined recursively as \(S_n^1\cong K_n\) and one obtains \(S_n^{t+1}\) from \(S_n^t\) by replacing each vertex from \(S_n^t\) by a copy of \(K_n\) and adding some special edges between these copies of \(K_n\). Let \(G\) be a graph.
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Roman [1,2]-domination of graphs

Applied Mathematics and Computation
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Guoliang Hao, Xiaodan Chen, Seyed Mahmoud Sheikholeslami, Haining Jiang   +3 more
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Trees with equal Roman {2}-domination number and independent Roman {2}-domination number

RAIRO - Operations Research, 2019
A Roman {2}-dominating function (R{2}DF) on a graph G =(V, E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to either at least one vertex v with f(v) = 2 or two vertices v1, v2 with f(v1) = f(v2) = 1. The weight of an R{2}DF f is the value w(f) = ∑u∈Vf(u).
Pu Wu, Zepeng Li, Zehui Shao, Seyed Mahmoud Sheikholeslami   +3 more
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Double Roman domination number

Discrete Applied Mathematics, 2018
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Anu V., Aparna Lakshmanan S.
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Roman Domination in Graphs

2020
This chapter is concerned with the concept Roman domination in graphs, which was introduced in 2004 by Cockayne, Dreyer, S.M. Hedetniemi, and S.T. Hedetniemi based on the strategies for defending the Roman Empire presented by Stewart (Sci Am 281:136–139, 1999) and ReVelle and Rosing (ReVelle CS, Rosing KE, Am Math Mon 107:585–594, 2000).
Mustapha Chellali, Nader Jafari Rad, Seyed Mahmoud Sheikholeslami, Lutz Volkmann   +3 more
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Perfect triple Roman domination

Discrete Applied Mathematics
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M. Kor, J. Amjadi, M. Chellali, S.M. Sheikholeslami   +3 more
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