A Characterization of Tree Type

Authors

Lon H. Mitchell, University of KansasFollow

Abstract

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.

Faculty Sponsor

Sivaram K. Narayan

Recommended Citation

Mitchell, Lon H. (2003) "A Characterization of Tree Type," Rose-Hulman Undergraduate Mathematics Journal: Vol. 4: Iss. 2, Article 5.
Available at: https://scholar.rose-hulman.edu/rhumj/vol4/iss2/5