A new upper bound on the total domination number of a graph.
Henning, Michael A., Yeo, Anders (2007)
The Electronic Journal of Combinatorics [electronic only]
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Henning, Michael A., Yeo, Anders (2007)
The Electronic Journal of Combinatorics [electronic only]
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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...
Yousef Alavi, Don R. Lick, Song Lin Tian (1989)
Mathematica Slovaca
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Bohdan Zelinka (1985)
Mathematica Slovaca
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Al-Addasi, S., Al-Ezeh, H. (2002)
International Journal of Mathematics and Mathematical Sciences
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Hamideh Aram, Sepideh Norouzian, Seyed Mahmoud Sheikholeslami (2013)
Discussiones Mathematicae Graph Theory
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Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-distance Roman dominating function on G is a labeling f : V (G) → {0, 1, 2} such that for every vertex with label 0, there is a vertex with label 2 at distance at most k from each other. The weight of a k-distance Roman dominating function f is the value w(f) =∑v∈V f(v). The k-distance Roman domination number of a graph G, denoted by γkR (D), equals the minimum weight of a k-distance Roman dominating...
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,...
Broderick Arneson, Piotr Rudnicki (2006)
Formalized Mathematics
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We are formalizing [9, pp. 81-84] where chordal graphs are defined and their basic characterization is given. This formalization is a part of the M.Sc. work of the first author under supervision of the second author.