R. Grone and R. Merris, Ordering trees by algebraic connectivity, Graphs & Combinatorics 6 (1990), 229-237. Research supported by Office of Naval Research contract 85-K-0335. Math Reviews 92a:05086.

Suppose G is a graph on n vertices. If D(G) = diag(d1,d2, ... ,dn) is the diagonal matrix of its vertex degrees and A(G) its adjacency matrix, then the Laplacian matrix L(G) = D(G) - A(G). The algebraic connectivity, a(G), is the second smallest eigenvalue of L(G). This article addresses the ordering of trees by their algebraic connectivities.

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