Monopolar graphs: Complexity of computing classical graph parameters

Barbato, Michele; Bezzi, Dario

doi:10.1016/j.dam.2020.12.023

Cited by 1 publication

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References 24 publications

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“…In this context, the graph partitioning problem is NP-complete [24], and there are available strategies based on spectral [25] (eigenproblem in [26]), combinatorial [27], geometric [28] and multi-level [29] heuristics. Partitioning of the graph vertices leads to recognition the of 2-subcolorable [30], bipartite [31], cluster [32], dominable [33], monopolar [34], r-partite [35], split [36], unipolar [37], trapezoid [38] and graphical algorithms (etc.) working efficiently with special classes of graphs that have been devised (for monopolar and 2-subcolorable in [30]; for unipolar and generalized split in [39]; for partitioning a big graph into k sub-graphs in [40,41]; for graph that does not contain an induced subgraph, a claw in [42]).…”

Section: Related Researchmentioning

confidence: 99%

Figures of Graph Partitioning by Counting, Sequence and Layer Matrices

2021

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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 C28 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.

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