On the chromatic number of integral circulant graphs

Authors:
Aleksandar Ilić;Milan Bašić
Affiliations:
Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia;Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

Integral circulant graphs are a generalization of unitary Cayley graphs, recently studied by Klotz and Sander. The integral circulant graph X"n(D) has vertices 0,1,...,n-1, and two vertices a and b are adjacent iff gcd(x-y,n)@?D, where D@?{d:d|n,1@?d=3, we construct a family of counterexamples using exhaustive search algorithm for graph coloring and disprove the conjecture in this case.