Constructions of triangular and quadrangular polyhedra of inscribable type
Ernest Jucovič, Sergej Ševec, Marián Trenkler (1997)
Mathematica Slovaca
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Ernest Jucovič, Sergej Ševec, Marián Trenkler (1997)
Mathematica Slovaca
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Peter John Owens (1998)
Mathematica Slovaca
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Siniša Vrećica (2005)
The Teaching of Mathematics
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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...
T. McKee (1988)
Fundamenta Mathematicae
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Stodolsky, B.Y. (2008)
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
Cheston, Grant A., Jap, Tjoen Seng (2006)
Journal of Graph Algorithms and Applications
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Endre Boros, Robert E. Jamison, Renu Laskar, Henry Martyn Mulder (2004)
Discussiones Mathematicae Graph Theory
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A vertex v in a graph G = (V,E) is k-simplicial if the neighborhood N(v) of v can be vertex-covered by k or fewer complete graphs. The main result of the paper states that a planar graph of order at least four has at least four 3-simplicial vertices of degree at most five. This result is a strengthening of the classical corollary of Euler's Formula that a planar graph of order at least four contains at least four vertices of degree at most five.