Sharp bounds on Zagreb indices of cacti with k pendant vertices

For a (molecular) graph, the first Zagreb index M-1 is equal to the sum of squares of its vertex degrees, and the second Zagreb index M-2 is equal to the sum of products of degrees of pairs of adjacent vertices. A connected graph G is a cactus if any two of its cycles have at most one common vertex. In this paper, we investigate the first and the second Zagreb indices of cacti with k pendant vertices. We determine sharp bounds for M-1-, M-2-values of n-vertex cacti with k pendant vertices. As a consequence, we determine the n-vertex cacti with maximal Zagreb indices and we also determine the cactus with a perfect matching having maximal Zagreb indices.