Abstract
It is shown that simple graphs gave equal topological information content if their automorphism groups are isomorphic. Further, if the automorphism groups of two graphs are represented by wreath products of which the inner groups are isomorphic, then the two graphs possess equal topological information content. Three graphs which correspond to organic molecules illustrate this finding.
Zusammenfassung
Wie gezeigt wird, besitzen schlichte Graphen gleichen topologischen Informationsgehalt, wenn ihre Automorphisgruppen isomorph sind. Ferner: sind die Automorphismengruppen zweier Graphen durch Kranzprodukte darstellbar deren Feingruppen isomorph sind, dann haben diese beiden Graphen gleichen topologischen Informationsgehalt. Drei Graphen, welche mit organischen Molekülen korrespondieren, illustrieren das Ergebnis.
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References and notes
Bonchev D., Information Theoretic Indices for Characterization of Chemical Structures, Chemometric Series (Bawden D., ed.), Vol. 5, p. 83, eq. (77). Chichester: Research Studies Press, J. Wiley. 1983.
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Dedicated to Professor Dr.Karl Schlögl on the occasion of his 60th birthday.
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Polansky, O.E. Note on the topological information content of simple graphs. Monatsh Chem 116, 211–216 (1985). https://doi.org/10.1007/BF00798456
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DOI: https://doi.org/10.1007/BF00798456