“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 15167 |
|
| Abstract: | |
|
Let k ≥ 1 and n1,…,nk ≥ 1 be some integers. Let S(n1,…,nk) be the tree T such that T has a vertex v of degree k and T\v is the disjoint union of the paths Pn1,…,Pnk, that is T\v ≅ Pn1∪…∪Pnk such that every neighbor of v in T has degree one or two.
The tree S(n1,…,nk) is called starlike tree, a tree with exactly one vertex of degree greater than two, if k ≥ 3. In this paper we obtain the eigenvalues of starlike trees. We obtain some bounds for the largest eigenvalue ( for the spectral radius) of starlike trees. In particular we prove that if
k ≥ 4 and n1,…,nk ≥ 2, then [(k−1)/(√{k−2})] < λ1(S(n1,…,nk)) < [(k)/(√{k−1})], where λ1(T) is the largest eigenvalue of T.
Finally we characterize all starlike trees that all of whose eigenvalues are in the interval (−2,2).
Download TeX format |
|
| back to top | |
