We study a random planar honeycomb lattice model, namely the random
double hexagonal chains. This is a lattice system with nonperiodic boundary
condition. The Wiener number is an important molecular descriptor based on
the distances, which was introduced by the chemist Harold Wiener in 1947.
By applying probabilistic method and combinatorial techniques we obtained
an explicit analytical expression for the expected value of Wiener number of a
random double hexagonal chain, and the limiting behaviors on the annealed
entropy of Wiener number when the random double hexagonal chain becomes
infinite in length are analyzed.
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