𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the eigenvalues of trees

✍ Scribed by L. Lovász; J. Pelikán


Book ID
105437430
Publisher
Springer Netherlands
Year
1973
Tongue
English
Weight
342 KB
Volume
3
Category
Article
ISSN
0031-5303

No coin nor oath required. For personal study only.


📜 SIMILAR VOLUMES


Sharp bounds on the eigenvalues of trees
✍ Shengbiao Hu 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 289 KB

Let λ 1 (T ) and λ 2 (T ) be the largest and the second largest eigenvalues of a tree T , respectively. We obtain the following sharp lower bound for λ 1 (T ): where d i is the degree of the vertex v i and m i is the average degree of the adjacent vertices of v i . Equality holds if and only if T i

On the two largest eigenvalues of trees
✍ M. Hofmeister 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 650 KB

Very little is known about upper bounds for the largest eigenvalues of a tree that depend only on the vertex number. Starting from a classical upper bound for the largest eigenvalue, some refinements can be obtained by successively removing trees from consideration. The results can be used to charac