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 16
For vertex connectivity ²V₂³V₂, (a) adjacency matrix [10] for the matrix-element combination (2 × 1)(2 × 2)(2 × 2¹), the corresponding proto-graph, the characteristic polynomial equations of the reduced proto-graphs and the resulting vertex subsets. (b), (c), (d) Three permutated versions of this adjacency matrix and proto-graph, and the characteristic polynomial equations of the reduced adjacency matrices. The characteristic polynomial equations of the reduced adjacency matrices in (b) and (c) are identical to those in (a) (adjacency matrix [10]), confirming that these proto-graphs are isomorphic. The characteristic polynomial equations for the reduced adjacency matrices derived from adjacency matrix [10′], shown in (d), are different, confirming that this proto-graph is non-isomorphic with the proto-graphs in (b) and (c).

FOUNDATIONS
ADVANCES

ISSN: 2053-2733

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

https://doi.org/10.1107/S2053273322001747

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