Geodesic
Remarks on spectral radius and Laplacian eigenvalues of a graph
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 781-790.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Let $G$ be a graph with $n$ vertices, $m$ edges and a vertex degree sequence $(d_1, d_2, \dots , d_n)$, where $d_1 \ge d_2 \ge \dots \ge d_n$. The spectral radius and the largest Laplacian eigenvalue are denoted by $\rho (G)$ and $\mu (G)$, respectively. We determine the graphs with \[ \rho (G) = \frac{d_n - 1}{2} + \sqrt{2m - nd_n + \frac{(d_n +1)^2}{4}} \] and the graphs with $d_n\ge 1$ and \[ \mu (G) = d_n + \frac{1}{2} + \sqrt {\sum _{i=1}^n d_i (d_i-d_n) + \Bigl (d_n - \frac{1}{2} \Bigr )^2}. \] We also present some sharp lower bounds for the Laplacian eigenvalues of a connected graph.
Classification : 05C07, 05C50, 05C75
Keywords: spectral radius; Laplacian eigenvalue; strongly regular graph 
@article{CMJ_2005__55_3_a18,
     author = {Zhou, Bo and Cho, Han Hyuk},
     title = {Remarks on spectral radius and {Laplacian} eigenvalues of a graph},
     journal = {Czechoslovak Mathematical Journal},
     pages = {781--790},
     publisher = {mathdoc},
     volume = {55},
     number = {3},
     year = {2005},
     mrnumber = {2153101},
     zbl = {1081.05068},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005__55_3_a18/}
}
TY  - JOUR
AU  - Zhou, Bo
AU  - Cho, Han Hyuk
TI  - Remarks on spectral radius and Laplacian eigenvalues of a graph
JO  - Czechoslovak Mathematical Journal
PY  - 2005
SP  - 781
EP  - 790
VL  - 55
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2005__55_3_a18/
LA  - en
ID  - CMJ_2005__55_3_a18
ER  - 
%0 Journal Article
%A Zhou, Bo
%A Cho, Han Hyuk
%T Remarks on spectral radius and Laplacian eigenvalues of a graph
%J Czechoslovak Mathematical Journal
%D 2005
%P 781-790
%V 55
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2005__55_3_a18/
%G en
%F CMJ_2005__55_3_a18
Zhou, Bo; Cho, Han Hyuk. Remarks on spectral radius and Laplacian eigenvalues of a graph. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 781-790. http://geodesic.mathdoc.fr/item/CMJ_2005__55_3_a18/