Abstract
The signless Laplacian matrix of a graph is defined to be the sum of its adjacency matrix and degree matrix. Let be the set of all the connected graphs of order n and diameter d and 𝒢 n,k the set of all connected graphs with order n and k cut vertices. In this article, we determine the graphs that have the maximal signless Laplacian spectral radius and give the upper bounds of graphs in these two sets.
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