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Distance Magic Cartesian Products of Graphs

100%

Cichacz S., Froncek D., Krop E., Raridan C.

Discussiones Mathematicae Graph Theory

2016

tom 36

nr 2

299-308

A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ : V → {1, . . . , n} such that the weight of every vertex v, computed as the sum of the labels on the vertices in the open neighborhood of v, is a constant. In this paper, we show that hypercubes with dimension divisible by four are not distance magic. We also provide some positive results by proving necessary and sufficient conditions for the Cartesian product of certain complete multipartite graphs and the cycle on four vertices to be distance magic.

Union of Distance Magic Graphs

84%

Cichacz S., Nikodem M.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 1

239-249

A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ from V to the set {1, . . . , n} such that the weight w(x) = ∑y∈NG(x) ℓ(y) of every vertex x ∈ V is equal to the same element μ, called the magic constant. In this paper, we study unions of distance magic graphs as well as some properties of such graphs.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Cichacz S.

1 Froncek D.

1 Krop E.

1 Nikodem M.

1 Raridan C.

1 2017

1 2016

Wyniki wyszukiwania

Distance Magic Cartesian Products of Graphs

Union of Distance Magic Graphs