The number of labelled -arch graphs.
Lamathe, Cédric (2004)
Journal of Integer Sequences [electronic only]
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Lamathe, Cédric (2004)
Journal of Integer Sequences [electronic only]
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Bohdan Zelinka (1978)
Mathematica Slovaca
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Bohdan Zelinka (1991)
Mathematica Bohemica
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Two types of a distance between isomorphism classes of graphs are adapted for rooted trees.
Cameron, Peter J. (1995)
The Electronic Journal of Combinatorics [electronic only]
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Damir Vukičević (2009)
Kragujevac Journal of Mathematics
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Brouwer, A.E. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Dariusz Dereniowski (2009)
Discussiones Mathematicae Graph Theory
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A vertex k-ranking of a simple graph is a coloring of its vertices with k colors in such a way that each path connecting two vertices of the same color contains a vertex with a bigger color. Consider the minimum vertex ranking spanning tree (MVRST) problem where the goal is to find a spanning tree of a given graph G which has a vertex ranking using the minimal number of colors over vertex rankings of all spanning trees of G. K. Miyata et al. proved in [NP-hardness proof and an approximation...
Xiaoling Zhang, Kecai Deng (2017)
Discussiones Mathematicae Graph Theory
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An L(2, 1, 1)-labeling of a graph G is an assignment of non-negative integers (labels) to the vertices of G such that adjacent vertices receive labels with difference at least 2, and vertices at distance 2 or 3 receive distinct labels. The span of such a labelling is the difference between the maximum and minimum labels used, and the minimum span over all L(2, 1, 1)-labelings of G is called the L(2, 1, 1)-labeling number of G, denoted by λ2,1,1(G). It was shown by King, Ras and Zhou...