The crossing number of image Original Research Article

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 image, Graphs and Combinatorics 18 (2) (2002) 381–394) have studied the crossing number of the generalized Petersen graph image and proved that image; image; image. In this paper, we study the crossing number of the circulant graph image and prove that image.