Abstract
Let Gω be a weighted graph, whose adjacency matrix and weighted degree diagnoal matrix are A(Gω) and D(Gω), respectively. For a given α∈[0,1], the matrix Aα(Gω)=αD(Gω)+(1−α)A(Gω) is the Aα-matrix of Gω. If all edge weights of Gω are belonging to (0,1), by defining the complement of Gω, we obtain some Nordhaus-Gaddum type bounds concerning Aα-eigenvalues of Gω.
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