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

Acta Crystallographica Section A
Acta Crystallographica
Section A FOUNDATIONS AND ADVANCES

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Figure 21
For vertex connectivity ¹V₁³V₃, (a) a proto-graph for the matrix-element combination (6 × 1)(2 × 2¹) and the corresponding vertex and edge subsets, (b) the directed proto-graph in which the 3–4 edge is assigned as wrapped in the +c direction and the corresponding adjacency matrix and edge subsets, and (c) the resultant chain graph. (d) The directed proto-graph in which the 3–4 and 1–2 edges have been 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 3–4 and 1–2 edges have been assigned as wrapped in the +c and −c directions, respectively, and the corresponding adjacency matrix and edge subsets, and (g) the resultant chain graph. Note that the chain graphs in (e) and (g) are isomorphic with the chain graph in (c). The blue arrows show the direction of unwrapping of the 1–2 edge in (e) the +c direction and in (g) the −c direction. All edges and vertices of a single repeat unit in each chain graph are shown in green and yellow, respectively. Legend as in Figs. 7

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FOUNDATIONS
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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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