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.
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