Graphical κ-tuple systems : Non-existence of the non-trivial graphical κ-tuple systems such that either 6≤κ≤8, or κ is less than or equal to the number of the vertices

Abstract

In this paper, it is proved, by using computer algebra system, that(1)there do not exist non-trivial graphical κ-tuple systems with 6≤κ≤8, and(2)if κ≥9, there do not exist non-trivial traphical κ-tuple systems such that κ is less than or equal to the number of the vertices. The results partially show the correctness of Chee's conjecture.