On walks in molecular graphs.

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Walks in molecular graphs and their counts for a long time have found applications in theoretical chemistry. These are based on the fact that the (i, j)-entry of the kth power of the adjacency matrix is equal to the number of walks starting at vertex i, ending at vertex j, and having length k. In recent papers (refs 13, 18, 19) the numbers of all walks of length k, called molecular walk counts, mwc k , and their sum from k = 1 to k = n - l, called total walk count, twc, were proposed as quantities suitable for QSPR studies and capable of measuring the complexity of organic molecules. We now establish a few general properties of mwc's and twc among which are the linear dependence between the mwc's and linear correlations between the mwc's and twc, the spectral decomposition of mwc's, and various connections between the walk counts and the eigenvalues and eigenvectors of the molecular graph. We also characterize the graphs possessing minimal and maximal walk counts.

Original languageEnglish
JournalJournal of Chemical Information and Computer Science
Volume41
Issue number3
Pages (from-to)739-745
Number of pages7
ISSN0095-2338
DOIs
Publication statusPublished - 05.04.2001
Externally publishedYes

DOI