For a (molecular) graph, the first Zagreb index M
1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M
2 is equal to the sum of products of degrees of pairs of adjacent vertices. In this paper, we investigate the first and the second Zagreb indices of maximal outerplanar graph. We determine sharp upper and lower bounds for M
1‐, M
2‐values among the n‐vertex maximal outerplanar graphs. As well we determine sharp upper and lower bounds of Zagreb indices for n‐vertex outerplanar graphs (resp. maximal outerplanar graphs) with perfect matchings.
