A subdivision theorem for vertices not on internal paths

作者：Gumbrell Lee^*

来源：Linear Algebra and Its Applications, 2013, 439(10): 2790-2794.

DOI：10.1016/j.laa.2013.09.005

• Subdivision
• Graph spectra
• Hoffman and Smith

In 1975 Hoffman and Smith showed that for a graph G not equal (D) over tilde (n) with an internal path, the value of the largest eigenvalue decreases strictly each time we subdivide the internal path. In this paper we extend this result to show that for a graph G not equal K-1,K-4 with a vertex of degree 4 or more, we can subdivide said vertex to create an internal path and the value of the largest eigenvalue also strictly decreases.

• 出版日期2013-11-15