Formula for the Hyper-Wiener Index on Rows of Unit Cells of the Face-Centred Cubic (FCC) Lattice

What is it about?

Wiener-index and hyper-Wiener index are essential topological indices which can be used to measure the compactness and expansiveness of molecules and also to predict some of their physical and chemical properties. While the Wiener index is computed as a linear function of the distances, the hyper-Wiener index uses also the second moment of the distances, in this way, giving relatively more weight to expanded structures than Wiener index, and therefore, it is a good predictor of effects that depend more than linearly on the physical size of a molecule. The face centered cubic (fcc) lattice is one of the most known crystallographic structure. In the paper, the hyper-Wiener index of graphs representing fcc unit cells connected to each other in a line is computed. According to the increasing number of unit cells, an integer sequence is also presented.

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Photo by Armand Khoury on Unsplash

Photo by Armand Khoury on Unsplash

Why is it important?

Graph indices can be used as structure descriptors, thus, it is good to know how to compute them for various graphs that are connected to structures of various materials.