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.
Dr. Sivaram K. Narayan, Central Michigan Universitysivaram.email@example.com
Mitchell, Lon H.
"A Characterization of Tree Type,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 4
, Article 5.
Available at: http://scholar.rose-hulman.edu/rhumj/vol4/iss2/5