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Abstract
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Random graphs play an important role in the study of graph theory. The two most common models are G(n; p) and G(n; m) random graphs. In this paper, we first introduce a graphic polynomial analogous to the degree sequence polynomial
and use it to compute the expected values of generalized first Zagreb indices for G(n; p) random graphs. Then we turn to G(n; m) random graphs and employ a different method to compute the expected values of the first Zagreb index and
of the forgotten index. Using the same approach we also compute the expected values of the second Zagreb index for both considered classes of random graphs. We validate our results by comparing them with results of numerical simulations
conducted over wide range of parameters.
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