Algebraic connectivity and degree sequences of trees
✍ Scribed by Türker Bıyıkoğlu; Josef Leydold
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 134 KB
- Volume
- 430
- Category
- Article
- ISSN
- 0024-3795
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In this paper, we first determine that the first four trees of order n 9 with the smallest algebraic connectivity are P n , Q n , W n and Z n with α(P n ) < α(Q n ) < α(W n ) < α(Z n ) < α(T ), where T is any tree of order n other than P n , Q n , W n , and Z n . Then we consider the effect on the L
[•] is a lower integer form and α depends on k. We show that every k-edge-connected graph with k ≥ 2, has a d k -tree, and α = 1 for k = 2, α = 2 for k ≥ 3.
## Abstract A graph __G__ is a 2‐tree if __G__ = __K__~3~, or __G__ has a vertex __v__ of degree 2, whose neighbors are adjacent, and __G__/ __v__ is a 2‐ tree. A characterization of the degree sequences of 2‐trees is given. This characterization yields a linear‐time algorithm for recognizing and r