Minimal size of a graph with diameter 2 and given maximal degree. II.
Znám, Š. (1992)
Acta Mathematica Universitatis Comenianae. New Series
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Znám, Š. (1992)
Acta Mathematica Universitatis Comenianae. New Series
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Hopkins, Glenn, Staton, William (1989)
International Journal of Mathematics and Mathematical Sciences
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Oleg V. Borodin, Anna O. Ivanova, Tommy R. Jensen (2014)
Discussiones Mathematicae Graph Theory
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It is known that there are normal plane maps M5 with minimum degree 5 such that the minimum degree-sum w(S5) of 5-stars at 5-vertices is arbitrarily large. In 1940, Lebesgue showed that if an M5 has no 4-stars of cyclic type (5, 6, 6, 5) centered at 5-vertices, then w(S5) ≤ 68. We improve this bound of 68 to 55 and give a construction of a (5, 6, 6, 5)-free M5 with w(S5) = 48
Ladislav Nebeský (1975)
Časopis pro pěstování matematiky
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Bohdan Zelinka (1986)
Mathematica Slovaca
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Ali Ahmad, E.T. Baskoro, M. Imran (2012)
Discussiones Mathematicae Graph Theory
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A total vertex irregular k-labeling φ of a graph G is a labeling of the vertices and edges of G with labels from the set {1,2,...,k} in such a way that for any two different vertices x and y their weights wt(x) and wt(y) are distinct. Here, the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x. The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G. We...
Ronald Dutton, William F. Klostermeyer (2013)
Discussiones Mathematicae Graph Theory
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Bipartite graphs with equal edge domination number and maximum matching cardinality are characterized. These two parameters are used to develop bounds on the vertex cover and total vertex cover numbers of graphs and a resulting chain of vertex covering, edge domination, and matching parameters is explored. In addition, the total vertex cover number is compared to the total domination number of trees and grid graphs.