TY - JOUR

T1 - Generalized wiener indices in hexagonal chains

AU - Sen-Peng, E. U.

AU - Yang, B. O.Yin

AU - Yeh, Yeong Nan

PY - 2006/2

Y1 - 2006/2

N2 - The Wiener index, or the Wiener number, also known as the "sum of distances" of a connected graph, is one of the quantities associated with a molecular graph that correlates nicely to physical and chemical properties, and has been studied in depth. An index proposed by Schultz is shown to be related to the Wiener index for trees, and Ivan Gutman proposed a modification of the Schultz index with similar properties. We deduce a similar relationship between these three indices for catacondensed benzenoid hydrocarbons (graphs formed of concatenated hexagons, or hexagonal chains, or sometimes acenes). Indeed, we may define three families of generalized Wiener indices, which include the Schultz and Modified Schultz indices as special cases, such that similar explicit formulae for all generalized Wiener indices hold on hexagonal chains. We accomplish this by first giving a more refined proof of the formula for the standard Wiener index of a hexagonal chain, then extending it to the generalized Wiener indices via the notion of partial Wiener indices. Finally, we discuss possible extensions of the result.

AB - The Wiener index, or the Wiener number, also known as the "sum of distances" of a connected graph, is one of the quantities associated with a molecular graph that correlates nicely to physical and chemical properties, and has been studied in depth. An index proposed by Schultz is shown to be related to the Wiener index for trees, and Ivan Gutman proposed a modification of the Schultz index with similar properties. We deduce a similar relationship between these three indices for catacondensed benzenoid hydrocarbons (graphs formed of concatenated hexagons, or hexagonal chains, or sometimes acenes). Indeed, we may define three families of generalized Wiener indices, which include the Schultz and Modified Schultz indices as special cases, such that similar explicit formulae for all generalized Wiener indices hold on hexagonal chains. We accomplish this by first giving a more refined proof of the formula for the standard Wiener index of a hexagonal chain, then extending it to the generalized Wiener indices via the notion of partial Wiener indices. Finally, we discuss possible extensions of the result.

KW - Generalized polynomial

KW - Generalized wiener indices

KW - Hex chain

KW - Wiener indices

KW - Wiener polynomial

UR - http://www.scopus.com/inward/record.url?scp=33645278373&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645278373&partnerID=8YFLogxK

U2 - 10.1002/qua.20732

DO - 10.1002/qua.20732

M3 - Article

AN - SCOPUS:33645278373

SN - 0020-7608

VL - 106

SP - 426

EP - 435

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

IS - 2

ER -