A note on the existence of cyclic and 1-rotational kite systems

作者：Yu, Aijun; Wang, Lingye; Wang, Su; Wang, Jinhua^*

来源：Ars Combinatoria, 2016, 126: 407-414.

• Kite system
• Skolem sequence
• Cycle kite system
• Rotational kite system

A kite graph is a graph obtained from a 3-cycle (or triple) by adding a pendent edge to a vertex of the 3-cycle. A kite system of order v is a pair (X, B), where B is an edge disjoint collection of kite graphs which partitions the edge set of K-v. A kite system of order v is cyclic if it admits an automorphism of order v, and 1-rotational if it admits an automorphism containing one fixed point and a cycle of length v - 1. In this paper, we show that there exists a cyclic kite system of order v if and only if v equivalent to 1 (mod 8), and there exists a 1-rotational kite system of order v if and only if v equivalent to 0 (mod 8).

• 出版日期2016-4
• 单位南通大学; 宿迁学院