Minimizing the least eigenvalue of bicyclic graphs with k pendant vertices

作者：Liu, Ruifang^*; Jia, Huicai; Shu, Jinlong

来源：Ars Combinatoria, 2012, 103: 19-32.

• Bicyclic graph
• Least eigenvalue
• Pendant vertices

Let B(n, k) be the set of bicyclic graphs with n vertices and k pendant vertices. In this paper, we determine the unique graph with minimal least eigenvalue among all graphs in B(n, k). This extremal graph is the same as that on the Laplacian spectral radius as done by Ji-Ming Guo[The Laplacian spectral radius of bicyclic graphs with n vertices and k pendant vertices, Science China Mathematics, 53(8)(2010)2135-2142]. Moreover, the minimal least eigenvalue is a decreasing function on k.

• 出版日期2012-1
• 单位河南工程学院; 郑州大学; 华东师范大学