0 Ju n 20 06 Divisor graphs have arbitrary order and size Le Anh Vinh School of Mathematics University of New South Wales Sydney 2052 Australia
نویسنده
چکیده
A divisor graph G is an ordered pair (V, E) where V ⊂ and for all u = v ∈ V , uv ∈ E if and only if u | v or v | u. A graph which is isomorphic to a divisor graph is also called a divisor graph. In this note, we will prove that for any n 1 and 0 m n 2 then there exists a divisor graph of order n and size m. We also present a simple proof of the characterization of divisor graphs which is due to Chartran, Muntean, Saenpholpant and Zhang.
منابع مشابه
O ct 2 00 5 On chromatic number of unit - quadrance graphs ( finite Euclidean graphs ) Le Anh Vinh School of Mathematics University of New South Wales Sydney 2052 NSW
The quadrance between two points A 1 = (x 1 , y 1) and A 2 = (x 2 , y 2) is the number Q(A 1 , A 2) = (x 1 − x 2) 2 + (y 1 − y 2) 2. Let q be an odd prime power and F q be the finite field with q elements. The unit-quadrance graph D q has the vertex set F 2 q , and X, Y ∈ F 2 q are adjacent if and only if Q(A 1 , A 2) = 1. Let χ(F 2 q) be the chromatic number of graph D q. In this note, we will...
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