On walks in molecular graphs.
Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet
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On walks in molecular graphs. / Gutman, Ivan; Rücker, Christoph; Rücker, Gerta .
in: Journal of Chemical Information and Computer Science, Jahrgang 41, Nr. 3, 05.04.2001, S. 739-745.Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet
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TY - JOUR
T1 - On walks in molecular graphs.
AU - Gutman, Ivan
AU - Rücker, Christoph
AU - Rücker, Gerta
PY - 2001/4/5
Y1 - 2001/4/5
N2 - 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.
AB - 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.
KW - Chemistry
UR - http://www.scopus.com/inward/record.url?scp=0035353668&partnerID=8YFLogxK
U2 - 10.1021/ci000149u
DO - 10.1021/ci000149u
M3 - Journal articles
VL - 41
SP - 739
EP - 745
JO - Journal of Chemical Information and Computer Sciences
JF - Journal of Chemical Information and Computer Sciences
SN - 0095-2338
IS - 3
ER -