Calculating the crossing number of a given graph is, in general, an elusive problem. As Garey and Johnson have proved, the problem of determining the crossing number of an arbitrary graph is NP-complete (Crossing number is NP-complete, SIAM J. Alg. Disc. Meth. 4 (1983) 312-316). The crossing numbers of very few families of graphs are known exactly. Richter and Salazar (The crossing number of P(N,3), Graphs and Combinatorics 18 (2) (2002) 381-394) have studied the crossing number of the generalized Petersen graph P(n,3) and proved that cr(P(3h,3))=h(h>=4); cr(P(3h+1,3))=h+3(h>=3); cr(P(3h+2,3))=h+2(h>=3). In this paper, we study the crossing number of the circulant graph C(n;{1,3}) and prove that cr(C(n;{1,3}))[email protected]?n/[email protected]?+nmod3(n>=8).
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