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Signless Laplacian spectral radii of graphs with given chromatic number

Signless Laplacian spectral radii of graphs with given chromatic number,10.1016/j.laa.2011.03.018,Linear Algebra and Its Applications,Guanglong Yu,Yar

Signless Laplacian spectral radii of graphs with given chromatic number   (Citations: 2)
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Let G be a simple graph with vertices v1,v2,…,vn, of degrees Δ=d1⩾d2⩾⋯⩾dn=δ, respectively. Let A be the (0,1)-adjacency matrix of G and D be the diagonal matrix diag(d1,d2,…,dn). Q(G)=D+A is called the signless Laplacian of G. The largest eigenvalue of Q(G) is called the signless Laplacian spectral radius or Q-spectral radius of G. Denote by χ(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 χ≠4,5,6,7 and the minimal Q-spectral radius are characterized as well.
Journal: Linear Algebra and Its Applications - LINEAR ALGEBRA APPL , vol. 435, no. 8, pp. 1813-1822, 2011
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