Wiener index of hexagonal systems

被引：494

作者：

Dobrynin, AA ^{[1
]}

Gutman, I

Klavzar, S

Zigert, P

机构：

[1] Russian Acad Sci, Siberian Branch, Sobolev Inst Math, Novosibirsk 630090, Russia

[2] Univ Kragujevac, Fac Sci, YU-34000 Kragujevac, Yugoslavia

[3] Univ Maribor, PEF, Dept Math, SI-2000 Maribor, Slovenia

来源：

ACTA APPLICANDAE MATHEMATICAE | 2002年 / 72卷 / 03期

关键词：

Wiener index; hexagonal system; hexagonal chain; catacondensed hexagonal system; isometric subgraph; congruence relation; Hosoya polynomial; algorithm;

D O I：

10.1023/A:1016290123303

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph. Hexagonal systems (HS's) are a special type of plane graphs in which all faces are bounded by hexagons. These provide a graph representation of benzenoid hydrocarbons and thus find applications in chemistry. The paper outlines the results known for W of the HS: method for computation of W, expressions relating W with the structure of the respective HS, results on HS's extremal w.r.t. W, and on integers that cannot be the W-values of HS's. A few open problems are mentioned. The chemical applications of the results presented are explained in detail.

引用

页码：247 / 294

页数：48

共 121 条

[1]

[Anonymous], 2000, DIMACS SER DISCRETE

[2]

[Anonymous], 1986, MATCH-COMMUN MATH CO

[3] A topological approach to predicting properties of infinite polymers.: Part VI.: Rational formulas for the normalized Wiener index and a comparison with index J [J].

Balaban, TS ;

Balaban, AT ;

Bonchev, D .

JOURNAL OF MOLECULAR STRUCTURE-THEOCHEM, 2001, 535 :81-92

[4]

BodrozaPantic O, 1996, ACH-MODELS CHEM, V133, P27

[5] TOPOLOGICAL CHARACTERIZATION OF CYCLIC STRUCTURES [J].

BONCHEV, D ;

MEKENYAN, O ;

TRINAJSTIC, N .

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, 1980, 17 (05) :845-893

[6]

BONCHEV D, 1987, MATCH-COMMUN MATH CO, V22, P209

[7]

Buckley F., 1990, Distance in Graphs

[8] TRIANGULATING A SIMPLE POLYGON IN LINEAR TIME [J].

CHAZELLE, B .

DISCRETE & COMPUTATIONAL GEOMETRY, 1991, 6 (05) :485-524

[9] On distances in benzenoid systems [J].

Chepoi, V .

JOURNAL OF CHEMICAL INFORMATION AND COMPUTER SCIENCES, 1996, 36 (06) :1169-1172

[10] Distances in benzenoid systems: Further developments [J].

Chepoi, V ;

Klavzar, S .

DISCRETE MATHEMATICS, 1998, 192 (1-3) :27-39

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