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Can I read Sharp Bounds on the Eigenvalues of Trees on EtoBox?
Sharp Bounds on the Eigenvalues of Trees by Shengbiao Hu is a Engineering article available to read on EtoBox.
What is Sharp Bounds on the Eigenvalues of Trees about?
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 is a tree Let d 1 and d 2 be the highest and the second highest degree of T , respectively. Let r (T ) be the maximum distance between the highest and the second highest degree vertices. We also show that if T is a tree of order (n > 2), then The equality holds if T is a tree T 1 or a tree T 2 , or T is a tree T 4 and d 1 = d 2 , where T 1 is formed by joining the centers of K 1,d 1 -1 and K 1,d 2 -1 and T 2 is formed by joining the centers of K 1,d 1 -1 and K 1,d 2 -1 to a new vertex, the T 4 is formed by joining a 1-degree vertex of K 1,d 1 and K 1,d 2 to a new vertex.
Who reads Sharp Bounds on the Eigenvalues of Trees?
It is typically read by researchers, students, and practitioners in Engineering.
- Author
- Shengbiao Hu
- Publisher
- Elsevier Science; Elsevier ; Elsevier Ltd.; Elsevier BV (ISSN 0898-1221)
- Published
- 2008
- Language
- EN
- Field
- Engineering (Physical Sciences)