A Property of $K_{2n+1}$ as the Sum of $n$ Spanning Cycles

Hatairat Yingtaweesittikul, Vites Longani

Abstract

It is known that  $K_{2n+1}$ is the sum of n spanning cycles. In this paper  we show that when 2n+1 is prime number we can have  additional property that all lines of the first cycle have distances 1,  all lines of the second cycle have distances 2, …., and all lines of the n-th cycle have distances n.  Also, when 2n+1 is not prime number, this property is not possible.