Connectivity and eigenvalues of graphs with given girth or clique number

Hong, Zhen-Mu; Lai, Hong‐Jian; Xia, Zheng-Jiang

doi:10.1016/j.laa.2020.08.015

Cited by 7 publications

(1 citation statement)

References 22 publications

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“…The accuracy of the model for 30 vertex cubic graphs after the exclusion of clique number from the dataset is 89.34 %, the precision of the standard cubic graph classification is 88.57 %, and the precision of the snark classification is 90 % with an overall Graph properties, which were most influential for the decision-making process were the girth of a graph, the Laplacian spectrum of a graph and the eigenvalues of the adjacency matrix of a graph. The authors of [15,18] specify these properties as having a relationship with the chromatic index for certain groups of graphs -most of which specify bounds on the chromatic index in relationship with one of the influential properties. The novelty of the findings of the presented study lies in the combination of these bounds with the use of machine learning models in order to find deeper relationships between the cubic graph properties.…”

Section: Graph Property Time Complexitymentioning

confidence: 99%

Interpretable random forest model for identification of edge 3-uncolorable cubic graphs

Dudáš,

Modrovičová

2024

Kybernetika

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Random forest is an ensemble method of machine learning that reaches a high level of accuracy in decision-making but is difficult to understand from the point of view of interpreting local or global decisions. In the article, we use this method as a means to analyze the edge 3colorability of cubic graphs and to find the properties of the graphs that affect it most strongly. The main contributions of the presented research are four original datasets suitable for machine learning methods, a random forest model that achieves 97.35% accuracy in distinguishing edge 3-colorable and edge 3-uncolorable cubic graphs, and the identification of crucial features of graph samples from the point of view of its edge colorability using Shapley values.

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Section: Graph Property Time Complexitymentioning

confidence: 99%