Displaying similar documents to “A census of vertices by generations in regular tessellations of the plane.”

Edge Dominating Sets and Vertex Covers

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.

5-Stars of Low Weight in Normal Plane Maps with Minimum Degree 5

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

On the Vertex Separation of Maximal Outerplanar Graphs

Markov, Minko (2008)

Serdica Journal of Computing

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We investigate the NP-complete problem Vertex Separation (VS) on Maximal Outerplanar Graphs (mops). We formulate and prove a “main theorem for mops”, a necessary and sufficient condition for the vertex separation of a mop being k. The main theorem reduces the vertex separation of mops to a special kind of stretchability, one that we call affixability, of submops.

The 1 , 2 , 3-Conjecture And 1 , 2-Conjecture For Sparse Graphs

Daniel W. Cranston, Sogol Jahanbekam, Douglas B. West (2014)

Discussiones Mathematicae Graph Theory

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The 1, 2, 3-Conjecture states that the edges of a graph without isolated edges can be labeled from {1, 2, 3} so that the sums of labels at adjacent vertices are distinct. The 1, 2-Conjecture states that if vertices also receive labels and the vertex label is added to the sum of its incident edge labels, then adjacent vertices can be distinguished using only {1, 2}. We show that various configurations cannot occur in minimal counterexamples to these conjectures. Discharging then confirms...