Ring Closure Matrix

Author(s): Milan Randic, Marjana Novic, Dejan Plavsic

Journal Name: Current Organic Chemistry

Volume 19 , Issue 3 , 2015


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Abstract:

We consider generalization of the terminal matrix of Zaretsky, in which only distances are listed between terminal vertices of acyclic graphs, to a condensed matrix for cyclic and polycyclic systems. Some 50 years ago Zaretsky has proved that the distance matrix between terminal vertices of acyclic graphs allows full reconstruction of the graph. We consider the question: Is there a subset of vertices in cyclic and polycyclic graphs which would allow from information on their distances a full reconstruction of the graph? As we report in this publication a distance matrix confined to a distance between the set of ring closure vertices may offer a positive answer to the considered problem.

Keywords: Adamantane, cyclic and polycyclic graphs, fibonacenes, ring closure matrix, ring closure vertices, zaretsky matrix.

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Article Details

VOLUME: 19
ISSUE: 3
Year: 2015
Published on: 12 March, 2015
Page: [274 - 281]
Pages: 8
DOI: 10.2174/1385272819666141216233128
Price: $65

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