Abstract
Let Fk denote the k-fan consisting of k triangles which intersect in exactly one common vertex, and Sn,k the complete split graph of order n consisting of a clique on k vertices and an independent set on the remaining vertices in which each vertex of the clique is adjacent to each vertex of the independent set. In this paper, it is shown that Sn,k is the unique graph attaining the maximum signless Laplacian spectral radius among all graphs of order n containing no Fk, provided that k≥2 and n≥3k2−k−2.
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