Topological indices of maximal outerplane graphs with two simplicial vertices

We explore the maximal outerplane graphs (MOP-graphs) with two simplicial vertices, laid out on the lattice of equilateral triangles (lattice MOPs, or LMOPs). Weak dual of LMOPs are isomorphic and similar to molecular graphs of isomers of conjugated polyene hydrocarbons (CPH). For this reason the LMOPs lend themselves to prognosticating properties of CPH. We suggest a new approach to search of multiple structure-property relationship (QSPR) correlations between topological indices (TI) of LMOPs from some given set and the physico-chemical parameters of isomers (CPH). The essence of such an approach lies in the initial selection of TI suitable for prognostication of properties of unbranched isomers CPH with subsequent search for structure-property correlations between already selected TI and physico-chemical parameters of isomers CPH. Such a methodology allows to eliminate unsuitable TIs, as well as physico-chemical parameters that poorly correlate with the 3D Wiener index. The fitness of the suggested approach has been proven through a computational experiment. Within the framework of the suggested approach we studied the TI of LMOP-graphs of $n=8,10,\dots,28$ orders, whose weak duals are isomorphic and geometrically similar to the molecular graphs of CPH model adopted in S.J. Cyvin (1996). From the multitude of Balaban, Wiener, Schultz, Randich, Harary and Zagreb group TIs simple $J$ and modified $J^{\prime}$ Balaban indices were selected.