An extension of Hoffman and Smith's subdivision theorem
Lee Gumbrell · arXiv (Cornell University) · 2012
In 1975 Hoffman and Smith showed that for a graph $G e\tilde{D}_n$ 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 $G e K_{1,4}$ 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.