群U_6n上Cayley图的完美边态转移

Perfect Edge State Transfer of Cayley Graphs over U_6n Groups

摘要

设U_6n=<a,b|a²ⁿ=b³=1,a^-1ba=b^-1>是一个有限群,1∉S⊂U_6n且S=S^-1={s^-1|s∈S}.利用图的谱理论和群的表示理论,研究群U_6n上Cayley图Cay(U_6n,S)的完美边态转移问题,并刻画了Cay(U_6n,S)上允许发生完美边态转移的充要条件.

Abstract

Let U_6n=<a,b|a²ⁿ=b³=1,a^-1ba=b^-1> be a finite group, 1∉S⊂U_6n and S=S^-1={s^-1|s∈S}. By using spectral theory and representation theory of groups, we study the perfect edge state transfer problem of Cayley graphs over U_6n groups, and characterize the necessary and sufficient conditions for allowing perfect edge state transfer to occur on Cay(U_6n,S).

关键词

Cayley图 / 完美边态转移 / 图的谱 / 群的表示

Key words

Cayley graph / perfect edge state transfer / spectrum of graph / representation of group

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基金资助

国家自然科学基金(11961040)

甘肃省自然科学基金(20JR5RA418)