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Survey of certain valuations of graphs

100%

Bača M., MacDougall J., Miller M., Slamin, Wallis W.

Discussiones Mathematicae Graph Theory

2000

tom 20

nr 2

219-229

The study of valuations of graphs is a relatively young part of graph theory. In this article we survey what is known about certain graph valuations, that is, labeling methods: antimagic labelings, edge-magic total labelings and vertex-magic total labelings.

Vertex-antimagic total labelings of graphs

86%

Bača M., MacDougall J., Bertault F., Miller M., Simanjuntak R., Slamin

Discussiones Mathematicae Graph Theory

2003

tom 23

nr 1

67-83

Open problem 1. For the paths Pₙ and the cycles Cₙ, determine if there is a vertex-antimagic total labeling for every feasible pair (a,d). Open problem 2. Apart from duality, how can a vertex-antimagic total labeling for a graph be used to construct another vertex-antimagic total labeling for the same graph, preferably with different a and d? Open problem 3. In Theorem 3, we found a way to construct VATL for a graph G from a vertex-magic total labeling of G. Are there other ways to do this? Open problem 4. Find, if possible, some structural characteristics of a graph which make a vertex-antimagic total labeling impossible

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Bača M.

2 MacDougall J.

2 Miller M.

2 Slamin

1 Bertault F.

1 Simanjuntak R.

1 Wallis W.

1 2003

1 2000

Wyniki wyszukiwania

Survey of certain valuations of graphs

Vertex-antimagic total labelings of graphs