1. Signless Laplacian spectral radii of graphs with given chromatic number
- Author
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Yu, Guanglong, Wu, Yarong, and Shu, Jinlong
- Subjects
- *
HARMONIC functions , *SPECTRAL theory , *RADIUS (Geometry) , *GRAPH theory , *NUMBER theory , *TOPOLOGICAL degree , *MATRICES (Mathematics) , *EIGENVALUES - Abstract
Abstract: Let G be a simple graph with vertices , of degrees , respectively. Let A be the -adjacency matrix of G and D be the diagonal matrix diag. is called the signless Laplacian of G. The largest eigenvalue of is called the signless Laplacian spectral radius or Q-spectral radius of G. Denote by 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 and the minimal Q-spectral radius are characterized as well. [Copyright &y& Elsevier]
- Published
- 2011
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