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Adjacency Matrix
Chromatic Number
Largest Eigenvalue
Spectral Radius
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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
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Signless Laplacian spectral radii of graphs with given chromatic number
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Citations: 2
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Guanglong Yu
,
Yarong Wu
,
Jinlong Shu
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 Qspectral 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 Qspectral radius are characterized, the extremal graphs with both the given
chromatic number
χ≠4,5,6,7 and the minimal Qspectral radius are characterized as well.
Journal:
Linear Algebra and Its Applications  LINEAR ALGEBRA APPL
, vol. 435, no. 8, pp. 18131822, 2011
DOI:
10.1016/j.laa.2011.03.018
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