Abstract
For given positive integers n, a 1,…, a m , we consider the undirected circulant graph G=( V, E) with set of vertices V={0,…, n−1} and set of edges E={[i,j] : i−j≡±a k ( mod n) for some 1⩽ k⩽ m}. We prove that G is planar if m=1 and non-planar if m⩾3. For m=2 we completely characterize planarity. It is shown that G is bipartite if and only if there is an l such that 2 l divides a 1,…,a m, 2 l+1|n , but 2 l+1∤a j for 1⩽ j⩽ m. If m⩽2, we also calculate the chromatic number of G.
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