Issue 9, 2008

Ravels: knot-free but not free. Novel entanglements of graphs in 3-space

Abstract

Molecular and extended framework materials, from proteins to catenanes and metal–organic frameworks, can assume knotted configurations in their bonding networks (the chemical graph). Indeed, knot theory and structural chemistry have remained closely allied, due to those connections. Here we introduce a new class of graph entanglement: “ravels”. These ravels—often chiral—tangle a graph without the presence of knots. Just as knots lie within cycles in the graph, ravels lie in the vicinity of a vertex. We introduce various species of ravels, including fragile ravels, composite ravels and shelled ravels. The role of ravels is examined in the context of finite and infinite graphs—analogous to molecular and extended framework nets—related to the diamond net.

Graphical abstract: Ravels: knot-free but not free. Novel entanglements of graphs in 3-space

Article information

Article type
Paper
Submitted
21 Dec 2007
Accepted
25 Apr 2008
First published
11 Jul 2008

New J. Chem., 2008,32, 1484-1492

Ravels: knot-free but not free. Novel entanglements of graphs in 3-space

T. Castle, M. E. Evans and S. T. Hyde, New J. Chem., 2008, 32, 1484 DOI: 10.1039/B719665B

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