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Stability Index

Definition

The stability index Z^_(G) of a graph G is defined by Z^_ = sum_(k = 0)^(⌊n/2⌋) left bracketing bar c_(2k) right bracketing bar , where c_k is the kth coefficient of the characteristic polynomial and ⌊n⌋ denotes the floor function. Unless otherwise stated, hydrogen atoms are usually ignored in the computation of such indices as organic chemists usually do when they write a benzene ring as a hexagon. The following table summarizes values of the Kirchhoff sum index for various special classes of graphs.

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