𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Signless Laplacian spectral radii of graphs with given chromatic number

✍ Scribed by Guanglong Yu; Yarong Wu; Jinlong Shu

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
263 KB
Volume
435
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

Let G be a simple graph with vertices v 1 , v 2 , . . . , v n , of degrees = ) is called the signless Laplacian spectral radius or Q -spectral radius of G. Denote by Ο‡(G) the chromatic number for a graph G. In this paper, for graphs with order n, the extremal graphs with both the given chromatic number and the maximal Q -spectral radius are characterized, the extremal graphs with both the given chromatic number Ο‡ = 4, 5, 6, 7 and the minimal Q -spectral radius are characterized as well.

πŸ“œ SIMILAR VOLUMES

The minimum signless Laplacian spectral
The minimum signless Laplacian spectral radius of graphs with given independence number
✍ Ruilin Li; Jinsong Shi πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 307 KB

The independence number Ξ±(G) of G is defined as the maximum cardinality of a set of pairwise non-adjacent vertices which is called an independent set. In this paper, we characterize the graphs which have the minimum spectral radius among all the connected graphs of order n with independence number Ξ±

On the signless Laplacian spectral radiu
On the signless Laplacian spectral radius of graphs with cut vertices
✍ Bao-Xuan Zhu πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 129 KB

In this paper, we show that among all the connected graphs with n vertices and k cut vertices, the maximal signless Laplacian spectral radius is attained uniquely at the graph G n,k , where G n,k is obtained from the complete graph K n-k by attaching paths of almost equal lengths to all vertices of