Let L(G) be the Laplacian matrix of a simple graph G. The characteristic valuation associated with the algebraic connectivity a(G) is used in classifying trees as Type I and Type II. We show a tree T is Type I if and only if its algebraic connectivity a(T) belongs to the spectrum of some branch B of T.

Author Bio

Lon Mitchell is currently a Madison and Lila Self Graduate Fellow at the University of Kansas. He holds an M.A. in mathematics from the University of Kansas, and a B.S. in mathematics and a B.M. in theory/composition from Central Michigan University.