In this paper, we show that if G is a starlike tree, then it is determined by its Laplacian spectrum. Moreover we prove some facts about trees with the same adjacency spectrum as a starlike tree.
On some forests determined by their Laplacian or signless Laplacian spectrum
✍ Scribed by Slobodan K. Simić; Zoran Stanić
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 571 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
✦ Synopsis
The largest eigenvalues a b s t r a c t
We consider the class of graphs whose each component is either a proper subgraph of some Smith graphs, or belongs to a precized subset of Smith graphs. We classify the graphs from the considered class into those which are determined, or not determined, by Laplacian, or signless Laplacian spectrum.
📜 SIMILAR VOLUMES
A tree is called double starlike if it has exactly two vertices of degree greater than 2. We denote by H n (p, p) (n ≥ 2, p ≥ 1) one special double starlike graph. In this work, graph H n (p, p) will be proved to be determined by its Laplacian spectrum.