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On defining numbers of circular complete graphs |
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| Authors: | Amir Daneshgar Hossein Hajiabolhassan |
| Affiliation: | a Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11365-9415, Tehran, Iran b Department of Mathematical Sciences, Shahid Beheshti University, P.O. Box 19834, Tehran, Iran c Department of Mathematics, Alzahra University, P.O. Box 1993891176, Tehran, Iran |
| Abstract: | Let d(σ) stand for the defining number of the colouring σ. In this paper we consider  and  for the onto χ-colourings γ of the circular complete graph Kn,d. In this regard we obtain a lower bound for dmin(Kn,d) and we also prove that this parameter is asymptotically equal to χ-1. Also, we show that when χ?4 and s≠0 then dmax(Kχd-s,d)=χ+2s-3, and, moreover, we prove an inequality relating this parameter to the circular chromatic number for any graph G. |
| Keywords: | 05C15 |
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