Minimum connected dominating sets of random cubic graphs.
Duckworth, W. (2002)
The Electronic Journal of Combinatorics [electronic only]
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Duckworth, W. (2002)
The Electronic Journal of Combinatorics [electronic only]
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Calamoneri, Tiziana, Jannelli, Simone, Petreschi, Rossella (1999)
Journal of Graph Algorithms and Applications
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Morgan, Kerri, Farr, Graham (2007)
Journal of Graph Algorithms and Applications
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Katarzyna Jesse-Józefczyk, Elżbieta Sidorowicz (2014)
Open Mathematics
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Consider a graph whose vertices play the role of members of the opposing groups. The edge between two vertices means that these vertices may defend or attack each other. At one time, any attacker may attack only one vertex. Similarly, any defender fights for itself or helps exactly one of its neighbours. If we have a set of defenders that can repel any attack, then we say that the set is secure. Moreover, it is strong if it is also prepared for a raid of one additional foe who can strike...
Maheshwari, Anil, Zeh, Norbert (2004)
Journal of Graph Algorithms and Applications
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Gajer, Pawel, Kobourov, Stephen G. (2002)
Journal of Graph Algorithms and Applications
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Vandenbussche, Jennifer, West, Douglas B. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Niessen, Thomas (2001)
The Electronic Journal of Combinatorics [electronic only]
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Changiz Eslahchi, Shahab Haghi, Nader Jafari (2014)
Discussiones Mathematicae Graph Theory
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A subset S of vertices in a graph G is called a total irredundant set if, for each vertex v in G, v or one of its neighbors has no neighbor in S −{v}. The total irredundance number, ir(G), is the minimum cardinality of a maximal total irredundant set of G, while the upper total irredundance number, IR(G), is the maximum cardinality of a such set. In this paper we characterize all cubic graphs G with irt(G) = IRt(G) = 2
Eiglsperger, Markus, Siebenhaller, Martin, Kaufmann, Michael (2005)
Journal of Graph Algorithms and Applications
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Prakash, V. (2005)
International Journal of Mathematics and Mathematical Sciences
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Chen, Hon-Chan (2004)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Seyed Sheikholeslami (2010)
Open Mathematics
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A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γ t(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt (G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. Karami, Khoeilar, Sheikholeslami and Khodkar,...