The signless Laplacian spectral radius of graphs with no intersecting triangles

Abstract

Let $F_k$ denote the $k$-fan consisting of $k$ triangles which intersect in exactly one common vertex, and $S_{n,k}$ 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 $S_{n,k}$ is the unique graph attaining the maximum signless Laplacian spectral radius among all graphs of order $n$ containing no $F_k$, provided that $k\ge 2$ and $n\ge 3k^2-k-2$.

10 pages

References in corpus (1)

• The spectral radius of graphs with no intersecting triangles