An Intermediate Value Theorem for the Decycling Numbers of Toeplitz Graphs

作者：Bau, Sheng^*; van Niekerk, Benjamin; White, David

来源：Graphs and Combinatorics, 2015, 31(6): 2037-2042.

DOI：10.1007/s00373-014-1492-3

• Cayley graphs
• Decycling number
• Intermediate value theorem
• Toeplitz graphs

In this paper we obtain an intermediate value theorem for the decycling numbers of Toeplitz graphs: if n = 3, and 0 = r = n -2, then there exists a Toeplitz graph of order n with decycling number r. We also prove that the decycling numbers of connected Cayley graphs of order n satisfy the intermediate value property if and only if n = 4 or 6.

• 出版日期2015-11
• 单位内蒙古民族大学