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To track the gradual change of the adjacency matrix of a simple graph G into the signless Laplacian matrix, V. Nikiforov in [35] suggested the study of the convex linear combination Aα (α-adjacency matrix),Aα(G)=αD(G)+(1−α)A(G), for α∈[0,1], where A(G) and D(G) are the adjacency and the diagonal vertex degrees matrices of G, respectively. Taking this definition as an idea the next matrix was considered...
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