The Number of Digraphs with Cycles of Length <i>k</i>

• 作 者: Chuanlong Wang Mudaster Sidik
• 机 构: DepartmentofMathematicalSciences,DepartmentofMathematics,DepartmentofMathematics
• 出 处: 离散数学期刊(英文)
• 发表日期: 2014年1期
• 关键词: ACYCLIC DIGRAPH EIGENVALUE Power DIGRAPH (0 1)-Matrix Acyclic DigraphEigenvalueP

In this note, we show that the number of digraphs with n vertices and with cycles of length k, 0 ≤ k ≤ n, is equal to the number of n × n (0,1)-matrices whose eigenvalues are the collection of copies of the entire kth unit roots plus, possibly, 0’s.