Sharp upper bounds on Zagreb indices of bicyclic graphs with a given matching number

For a (molecular) graph, the first Zagreb index M1M1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M2M2 is equal to the sum of products of degrees of pairs of adjacent vertices. In this paper, we investigate Zagreb indices of bicyclic graphs with a given matching number. Sharp upper bounds for the first and second Zagreb indices of bicyclic graphs in terms of the order and given size of matching are determined, respectively.