About a criterion of equality to 3 for exponent of regular primitive graph | Applied Discrete Mathematics. Supplement. 2019. № 12. DOI: 10.17223/2226308X/12/51

About a criterion of equality to 3 for exponent of regular primitive graph

This paper presents some results related to finding criterion of equality to 3 for the exponent of regular primitive graph. Several necessary and several sufficient conditions are found. We show that no one of them could be criterion. For that purpose, we have also run a computation experiment for counting the number of primitive regular graphs with the exponent 3, that don't satisfied those conditions. As for a graph of the diameter 2, the following criterion is found for it: graph with diameter 2 is primitive with exponent 3 iff each vertex in that graph lies on at least one cycle of length 3 and there is at least one edge that does not lie on cycles with length 3.

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Keywords

примитивный граф, регулярный граф, экспонент графа, primitive graph, regular graph, graph exponent

Authors

Name	Organization	E-mail
Los I. V.	Saratov State University	los.ilia.ru@gmail.com
Abrosimov M. B.	Saratov State University	mic@rambler.ru

Всего: 2

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