Walk counts, labyrinthicity, and complexity of acyclic and cyclic graphs and molecules

被引：52

作者：

Rücker, G ^{[1
]}

Rücker, C ^{[1
]}

机构：

[1] Univ Freiburg, Inst Organ Chem & Biochem, D-79104 Freiburg, Germany

来源：

JOURNAL OF CHEMICAL INFORMATION AND COMPUTER SCIENCES | 2000年 / 40卷 / 01期

关键词：

D O I：

10.1021/ci9900579

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

It is demonstrated how the complexity of a (molecular) graph can be quantified in terms of the walk counts, extremely easily obtained graph invariants that depend on size, branching, cyclicity, and edge and vertex weights (unsaturation, heteroatoms). The influence of symmetry is easily accounted for. The term labyrinthicity is proposed for what is measured by walk counts alone, neglecting symmetry. The total walk count and recently advanced measures of labyrinthicity or complexity are compared with respect to the ordering of structures and to the computational effort required to obtain numerical values.

引用

页码：99 / 106

页数：8

共 44 条

[1]

[Anonymous], ALGEBRAIC COMBINATOR

[2] Rigorous mathematical approaches to strategic bonds and synthetic analysis based on conceptually simple new complexity indices [J].

Bertz, SH ;

Sommer, TJ .

CHEMICAL COMMUNICATIONS, 1997, (24) :2409-2410

[3] THE 1ST GENERAL INDEX OF MOLECULAR COMPLEXITY [J].

BERTZ, SH .

JOURNAL OF THE AMERICAN CHEMICAL SOCIETY, 1981, 103 (12) :3599-3601

[4] BRANCHING IN GRAPHS AND MOLECULES [J].

BERTZ, SH .

DISCRETE APPLIED MATHEMATICS, 1988, 19 (1-3) :65-83

[5]

BERTZ SH, IN PRESS MATCH COMMU

[6]

BERTZ SH, 1986, ARTIF INTELL, P169

[7]

BERTZ SH, 1993, ORGANIC SYNTHESIS TH, V2, P67

[8]

Bertz SH, 1983, CHEM APPL TOPOLOGY G, P206

[9] MOLECULAR CYCLICITY AND CENTRICITY OF POLYCYCLIC GRAPHS .1. CYCLICITY BASED ON RESISTANCE DISTANCES OR RECIPROCAL DISTANCES [J].

BONCHEV, D ;

BALABAN, AT ;

LIU, XY ;

KLEIN, DJ .

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, 1994, 50 (01) :1-20

[10] TOPOLOGICAL ORDER IN MOLECULES .1. MOLECULAR BRANCHING REVISITED [J].

BONCHEV, D .

THEOCHEM-JOURNAL OF MOLECULAR STRUCTURE, 1995, 336 (2-3) :137-156

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