The six classes of trees with the largest algebraic connectivity
โ Scribed by Xi-Ying Yuan; Jia-Yu Shao; Li Zhang
- Book ID
- 108112699
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 184 KB
- Volume
- 156
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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 ฮฑ(P n ) < ฮฑ(Q n ) < ฮฑ(W n ) < ฮฑ(Z n ) < ฮฑ(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
## Abstract We prove that every connected graph __G__ contains a tree __T__ of maximum degree at most __k__ that either spans __G__ or has order at least __k__ฮด(__G__) + 1, where ฮด(__G__) is the minimum degree of __G.__ This generalizes and unifies earlier results of Bermond [1] and Win [7]. We als