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Based on two trivial observations of the AEC industry, this paper proposes atraversal method ("S-rule") and expression ("1-dimensional-graph") transformedfrom DFS. This traversal method conforms to the original cognitive logic of theAEC industry, and the 1-d expression has clear language characteristics whilecompletely retaining the topological relationship of the planar graph : asequence of finite symbols (vocabularies) under definite rules. Moreover, thelanguage can be restored to a standard 2-d form that is isomorphic to theoriginal planar graph, thus ensuring its visualization characteristics.Fragments of the 1-d language can be used as planar units for free combinationand weighting, and as the data foundation to support advanced calculationsincluding FEM and isomorphic matching. And after the 2-d graph is reduced to1-d, any 3-d or higher-dimensional graphs can also be reduced to 1 or 2dimensions. The first half of this paper (Chapter 1) takes the 4X4 standardgrid as an example to introduce the prototype of S-rule and 1-d expression, andgives the mapping rule from 1-d expression to its editable text form. In thesecond half of this paper, the rule and expression are gradually extended tonon-embedded planar graphs (Chapter 2) and embedded planar graphs (Chapter 3),and the "grammar" is finally summarized (Chapter 4).

The S-rule and 1-d representation for the traversal of a planar graph in AEC industry