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.
Graphical Abstract
Call for Papers in Thematic Issues
Catalytic C-H bond activation as a tool for functionalization of heterocycles
The major topic is the functionalization of heterocycles through catalyzed C-H bond activation. The strategies based on C-H activation not only provide straightforward formation of C-C or C-X bonds but, more importantly, allow for the avoidance of pre-functionalization of one or two of the cross-coupling partners. The beneficial impact of ...read more
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