The Padmakar–Ivan (PI) index is a graph invariant defined as the summation of the sums of n eu (e|G) and n ev (e|G) over all the edges e = uv of a connected graph G, i.e., PI(G) = ∑ e∈E(G)[n eu (e|G) + n ev (e|G)], where n eu (e|G) is the number of edges of G lying closer to u than to v and n ev (e|G) is the number of edges of G lying closer to v than to u. An efficient formula for calculating the PI index of phenylenes is given, and a simple relation is established between the PI index of a phenylene and of the corresponding hexagonal squeeze.
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Deng, H., Chen, S. & Zhang, J. The PI index of phenylenes. J Math Chem 41, 63–69 (2007). https://doi.org/10.1007/s10910-006-9198-2
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DOI: https://doi.org/10.1007/s10910-006-9198-2