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Atomic walk counts of negative order.

István Lukovits1, Nenad Trinajstić

  • 1Chemical Research Center, H-1525 Budapest, P.O.B. 17, Hungary. lukovits@chemres.hu

Journal of Chemical Information and Computer Sciences
|July 23, 2003
PubMed
Summary

Atomic walk counts (awc's) and molecular walk counts (mwc's) were extended to negative orders using a backward algorithm. This method works even for singular matrices, allowing for noninteger and negative values in these extended walk counts.

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Area of Science:

  • Chemical graph theory
  • Computational chemistry
  • Network analysis

Background:

  • Atomic walk counts (awc's) and molecular walk counts (mwc's) quantify walks in molecular structures.
  • Existing methods primarily focus on non-negative integer orders (k >= 1).

Purpose of the Study:

  • To extend the concepts of atomic and molecular walk counts to zero and negative orders.
  • To develop a robust method applicable even when the adjacency matrix is singular.

Main Methods:

  • Utilized a backward algorithm, adapting the standard procedure for calculating mwc's.
  • Applied the algorithm to extend awc's and mwc's to zero and negative orders.

Main Results:

  • Successfully extended awc's and mwc's to zero and negative orders.
  • Demonstrated the algorithm's efficacy with singular adjacency matrices.
  • Observed that negative order awc's and mwc's can yield noninteger and negative values.
  • Noted that zero order awc's may deviate from one when the adjacency matrix is singular.

Conclusions:

  • The backward algorithm provides a generalizable method for calculating extended atomic and molecular walk counts.
  • This extension broadens the applicability of walk count analysis in chemical graph theory and network science.
  • The findings offer new perspectives on molecular descriptors derived from graph structures.

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