Some colouring problems for unit-quadrance graphs
نویسنده
چکیده
The quadrance between two points A1 = (x1, y1) and A2 = (x2, y2) is the number Q(A1, A2) = (x1 − x2) + (y1 − y2). Let q be an odd prime power and Fq be the finite field with q elements. The unit-quadrance graph Dq has the vertex set F 2 q , and X,Y ∈ F 2 q are adjacent if and only if Q(A1, A2) = 1. In this paper, we study some colouring problems for the unit-quadrance graph Dq and discuss some open problems.
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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تاریخ انتشار 2006