On the signless Laplacian index of cacti with a given number of pendant vertices

A connected graph G is a cactus if any two of its cycles have at most one common vertex. In this article, we determine graphs with the largest signless Laplacian index among all the cacti with n vertices and k pendant vertices. As a consequence, we determine the graph with the largest signless Laplacian index among all the cacti with n vertices; we also characterize the n-vertex cacti with a perfect matching having the largest signless Laplacian index.