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We introduce the reduced second hyper-Zagreb index of a graph. Considering this index, we define the reduced second hyper-Zagr eb polynomial of a graph. Also we define the reduced second Zagreb polynomial of a gr aph. In this paper, we compute the reduced second hyper-Zagreb index and its polynomia l of certain families of networks such as silicate and chain silicate networks. Also we determine the reduced second Zagreb polynomial of certain silicate networks.

Reduced Second Hyper-Zagreb Index and its Polynomial of Certain Silicate Networks