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There has been an upsurge of research on complex networks in recent years.The purpose of this paper is to study the mathematical properties of the randomchain networks PGn with the help of graph theory. We first solve the expectedvalue expressions of the Gutman index, Schultz index, multiplicativedegree-Kirchhoff index and additive degree-Kirchhoff index, and then we get theexplicit expression formulas of their variances. Finally, we find that theirlimiting distributions all have the probabilistic and statistical significanceof normal distribution.

The expected values, variances and limiting distributions of Gutman  index, Schultz index, multiplicative degree-Kirchhoff index and additive  degree-Kirchhoff index for a class of random chain networks