The normalized algebraic connectivity of a graph G, denoted by λ2(G), is the second smallest eigenvalue of its normalized Laplacian matrix. In this paper, we firstly determine all trees with λ2(G)≥1-63. Then we classify such trees into six classes C1,...,C6 and prove that λ2( Ti)>λ2(Tj) for 1≤i<j≤6, where Ti∈Ci and Tj∈Cj. At the same time, the values of the normalized algebraic connectivity for the six classes of trees are provided, respectively. These results are similar to those on the algebraic connectivity which were obtained by Yuan et al. (2008) .
Scopus Subject Areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Normalized algebraic connectivity