Abstract
ABSTRACT Let G be a simple graph of order n with m edges. Denote by the diagonal matrix of its vertex degrees and by its adjacency matrix. Then the signless Laplacian matrix of G is . Let be the signless Laplacian eigenvalues of graph G and also let be the largest positive integer such that . Denote by the complement graph of graph G. If , then we prove that . Moreover, if , then .
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