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Volumn 73, Issue 4, 2000, Pages 909-921

On the Zagreb Indices as Complexity Indices

Author keywords

Complexity indices; Molecular graphs; Saturated hydrocarbons; Zagreb indices

Indexed keywords


EID: 0001486089     PISSN: 00111643     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (55)

References (35)
  • 10
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    • second printing, Addison-Wesley, Reading, MA
    • F. Harary, Graph Theory, second printing, Addison-Wesley, Reading, MA, 1972.
    • (1972) Graph Theory
    • Harary, F.1
  • 14
    • 0442303361 scopus 로고    scopus 로고
    • note
    • A walk on a graph is an alternating sequence of vertices and edges beginning and ending with vertices, in which each edge is incident with two vertices immediately preceding and following it. A self-returning walk is a walk starting and ending at the same vertex.
  • 15
    • 0141510916 scopus 로고
    • Branching is an intuitive concept not uniquely defined (e.g., J. W. Essam and M. E. Fisher, Rev. Mod. Phys. 42 (1970) 272-305), though it can be identified through the appearance of vertices of degrees three and higher.
    • (1970) Rev. Mod. Phys. , vol.42 , pp. 272-305
    • Essam, J.W.1    Fisher, M.E.2
  • 16
    • 0000110023 scopus 로고
    • One can look upon cyclicity as a kind of structural change resembling branching in that the values of degrees of some vertices within the cycle increase from two to three and higher at the sites of bridging cycle. This structural characteristic has been named (D. Bonchev, Bulg. Chem. Comm. 28 (1995) 567-582) an internal branching. Therefore, the degree of a vertex in a cycle can increase either by cyclization (the internal branching) or by attaching to it acyclic, cyclic or spiro-cyclic fragments (the external branching). These three possibilities correspond, for example, to cyclohexane → bicyclo[2.2.0]hexane, cyclohexane → isopropylcyclohexane and cyclohexane → spiro[3.5]nonane.
    • (1995) Bulg. Chem. Comm. , vol.28 , pp. 567-582
    • Bonchev, D.1
  • 17
    • 0442318895 scopus 로고    scopus 로고
    • K. Mainzer, Hyle 3 (1997) 29-49.
    • (1997) Hyle , vol.3 , pp. 29-49
    • Mainzer, K.1
  • 18
    • 0012480214 scopus 로고    scopus 로고
    • On the Concept of Molecular Complexity
    • in press
    • M. Randić, On the Concept of Molecular Complexity, Croat. Chem. Acta, in press.
    • Croat. Chem. Acta
    • Randić, M.1
  • 26
    • 0002531454 scopus 로고
    • D. H. Rouvray (Ed.), Nova Sci. Publ., Commack, N.Y.
    • D. Bonchev, in: D. H. Rouvray (Ed.), Computational Chemical Graph Theory, Nova Sci. Publ., Commack, N.Y., 1990, pp. 33-63.
    • (1990) Computational Chemical Graph Theory , pp. 33-63
    • Bonchev, D.1
  • 29
    • 0442271896 scopus 로고    scopus 로고
    • note
    • The rules used are: (i) branched trees are more complex than unbranched trees; (ii) trees with several branches are more complex than trees with a single branch; (iii) cyclic structures are more complex than the corresponding acyclic structures; (iv) bicyclic structures are more complex than monocyclic structures; (v) branched cycles are more complex than cycles without branches and (vi) cycles with several external branches are more complex than cycles with a single branch.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.