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Journal of Mathematical Chemistry

, Volume 41, Issue 1, pp 63–69 | Cite as

The PI index of phenylenes

  • Hanyuan Deng
  • Shubo Chen
  • Jie Zhang
Article

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) = ∑ eE(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.

Keywords

PI index phenylene hexagonal squeeze 

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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.College of Mathematics and Computer ScienceHunan Normal UniversityHunanPeople’s Republic China

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