Abstract
Research on Q-spectral and L-spectral radius of graph has been attracted many attentions. In other hand, several graphs associated with group have been introduced. Based on the absence of research on Q-spectral and L-spectral radius of subgroup graph of dihedral group, we do this research. We compute Q-spectral and L-spectral radius of subgroup graph of dihedral group and their complement, for several normal subgroups. Q-spectrum and Lspectrum of these graphs are also observed and we conclude that all graphs we discussed in this paper are Q-integral dan L-integral.
Highlights
For finite simple graph G of order p, its signless Laplacian matrix is defined by Q(G) = D(G) + A(G) and its Laplacian matrix is defined by L(G) = D(G) – A(G), where D(G) is the vertex degree of G and A(G) is adjacency matrix of G
Q-spectral and L-spectral radius have received a great deal of attention and several researches have been reported
Some researches on Q-spectral radius and its sharp bound for various graphs can be seen in [1,2,3,4]
Summary
Research on Q-spectral and L-spectral radius of graph has been attracted many attentions. Several graphs associated with group have been introduced. Based on the absence of research on Q-spectral and L-spectral radius of subgroup graph of dihedral group, we do this research. We compute Q-spectral and L-spectral radius of subgroup graph of dihedral group and their complement, for several normal subgroups.
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