Abstract
The signless Laplacian spectral radius of a graph is the largest eigenvalue of its signless Laplacian matrix. In the paper, the graph with maximal signless Laplacian spectral radius among all graphs with given size and clique number is characterized. As applications, we determine the graph with maximal signless Laplacian spectral radius among all graphs with given size, and characterize the graph with maximal signless Laplacian spectral radius among all graphs with given size and chromatic number.
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