On walks in molecular graphs.

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On walks in molecular graphs. / Gutman, Ivan; Rücker, Christoph; Rücker, Gerta .
In: Journal of Chemical Information and Computer Science, Vol. 41, No. 3, 05.04.2001, p. 739-745.

Research output: Journal contributionsJournal articlesResearchpeer-review

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Gutman I, Rücker C, Rücker G. On walks in molecular graphs. Journal of Chemical Information and Computer Science. 2001 Apr 5;41(3):739-745. doi: 10.1021/ci000149u

Bibtex

@article{f336dc7d42c84d04b3d3dfa132698ddc,
title = "On walks in molecular graphs.",
abstract = "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. ",
keywords = "Chemistry",
author = "Ivan Gutman and Christoph R{\"u}cker and Gerta R{\"u}cker",
year = "2001",
month = apr,
day = "5",
doi = "10.1021/ci000149u",
language = "English",
volume = "41",
pages = "739--745",
journal = "Journal of Chemical Information and Computer Science",
issn = "0095-2338",
publisher = "American Chemical Society",
number = "3",

}

RIS

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 Science

JF - Journal of Chemical Information and Computer Science

SN - 0095-2338

IS - 3

ER -

DOI