Figures of Graph Partitioning by Counting, Sequence and Layer Matrices

Mihaela Aurelia Tomescu, Lorentz Jäntschi and Doina Iulia Rotaru
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Mihaela Aurelia Tomescu: Department of Mathematics-Informatics, University of Petrosani, 332006 Petrosani, Romania
Lorentz Jäntschi: Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania
Doina Iulia Rotaru: Department of Conservative Dentistry, “Iuliu Hatieganu” Medicine and Pharmacy University, 400349 Cluj-Napoca, Romania

Mathematics, 2021, vol. 9, issue 12, 1-25

Abstract: A series of counting, sequence and layer matrices are considered precursors of classifiers capable of providing the partitions of the vertices of graphs. Classifiers are given to provide different degrees of distinctiveness for the vertices of the graphs. Any partition can be represented with colors. Following this fundamental idea, it was proposed to color the graphs according to the partitions of the graph vertices. Two alternative cases were identified: when the order of the sets in the partition is relevant (the sets are distinguished by their positions) and when the order of the sets in the partition is not relevant (the sets are not distinguished by their positions). The two isomers of C 28 fullerenes were colored to test the ability of classifiers to generate different partitions and colorings, thereby providing a useful visual tool for scientists working on the functionalization of various highly symmetrical chemical structures.

Keywords: graph partitioning; counting matrices; sequence matrices; layer matrices; molecular topology; molecular similarity; molecular symmetry (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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