The spectral radius of graphs without trees of diameter at most four
Abstract
Nikiforov (LAA, 2010) conjectured that for given integer $k$, any graph $G$ of sufficiently large order $n$ with spectral radius $\mu(G)\geq \mu(S_{n,k})$ contains all trees of order $2k+2$, unless $G=S_{n,k}$, where $S_{n,k}=K_k\vee \overline{K_{n-k}}$, the join of a complete graph of order $k$ and an empty graph of order $n-k$. In this paper, we show that the conjecture is true for trees of diameter at most four.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2016
- DOI:
- 10.48550/arXiv.1610.00833
- arXiv:
- arXiv:1610.00833
- Bibcode:
- 2016arXiv161000833H
- Keywords:
-
- Mathematics - Combinatorics;
- 05C50;
- 05C35
- E-Print:
- 10 pages