Bond topology of chain, ribbon and tube silicates. Part I. Graph-theory generation of infinite one-dimensional arrangements of (TO4)n− tetrahedra

Day, M.C.; Hawthorne, F.C.

doi:10.1107/S2053273322001747

Figure 26
For vertex connectivity ³V₂⁴V₁, (a) a proto-graph for the matrix-element combination (4 × 1)(2 × 1)(2 × 2¹) and its vertex and edge subsets, (b) the directed proto-graph in which the 2–3 edge is assigned as wrapped in the +c direction, its corresponding adjacency matrix and edge subsets, and (c) the resultant chain graph. (d) The directed proto-graph in which the 2–3 edge is assigned as wrapped in the +c direction and the 1–2 edge is assigned as wrapped in the −c direction, and the corresponding adjacency matrix and edge subsets, and (e) the resultant chain graph. (f) The directed proto-graph in which the 2–3 and 1–2 edges are assigned as wrapped in the +c direction, its corresponding adjacency matrix and edge subsets, and (g) the resultant chain graph. (h) The directed proto-graph in which the 2–3, 1–2 and 1–3 edges are assigned as wrapped in the +c direction, its corresponding adjacency matrix and edge subsets, and (i) the resultant chain graph. Note that the chain graphs in (e) and (i) are isomorphic with the chain graph in (c) as the unwrappings involving vertex 2 in (d) are redundant and the unwrappings involving vertex 1 in (h) are redundant. Legend as in Figs. 7

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ISSN: 2053-2733

Volume 78| Part 3| May 2022| Pages 212-233

https://doi.org/10.1107/S2053273322001747

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