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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Displaying similar documents to “Decomposition of complete graphs into factors of diameter two”
Minimal size of a graph with diameter 2 and given maximal degree. II.
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Hopkins, Glenn, Staton, William (1989)
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5-Stars of Low Weight in Normal Plane Maps with Minimum Degree 5
Oleg V. Borodin, Anna O. Ivanova, Tommy R. Jensen (2014)
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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
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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...