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Characterizing which Powers of Hypercubes and Folded Hyper- cubes Are Divisor Graphs

100%

AbuHijleh E. A., AbuGhneim O. A., Al-Ezeh H.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 2

301-311

In this paper, we show that Qkn is a divisor graph, for n = 2, 3. For n ≥ 4, we show that Qkn is a divisor graph iff k ≥ n − 1. For folded-hypercube, we get FQn is a divisor graph when n is odd. But, if n ≥ 4 is even integer, then FQn is not a divisor graph. For n ≥ 5, we show that (FQn)k is not a divisor graph, where 2 ≤ k ≤ [n/2] − 1.

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Vertex coloring the square of outerplanar graphs of low degree

100%

Agnarsson G., Halldórsson M.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 4

619-636

Vertex colorings of the square of an outerplanar graph have received a lot of attention recently. In this article we prove that the chromatic number of the square of an outerplanar graph of maximum degree Δ = 6 is 7. The optimal upper bound for the chromatic number of the square of an outerplanar graph of maximum degree Δ ≠ 6 is known. Hence, this mentioned chromatic number of 7 is the last and only unknown upper bound of the chromatic number in terms of Δ.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 AbuGhneim O. A.

1 AbuHijleh E. A.

1 Agnarsson G.

1 Al-Ezeh H.

1 Halldórsson M.

1 2015

1 2010

Wyniki wyszukiwania

Characterizing which Powers of Hypercubes and Folded Hyper- cubes Are Divisor Graphs

Vertex coloring the square of outerplanar graphs of low degree