On some results of the study of F-irregular graphs in the class of  biconnected graphs F

  • Tatiana S. Dovzhenok Secondary school No. 30 of Gomel, 6 Piaсdziasiat gadow BSSR Street, Gomiel 246032, Belarus
  • Artem V. Filuta Secondary school No. 30 of Gomel, 6 Piaсdziasiat gadow BSSR Street, Gomiel 246032, Belarus
  • Nastassia E. Chuhai Secondary school No. 30 of Gomel, 6 Piaсdziasiat gadow BSSR Street, Gomiel 246032, Belarus

Abstract

We consider herein the well-known problem of F-irregular graphs in relation to the class of biconnected graphs F. It is established that for any natural n ≥ 8 there exists a K3-irregular graph of order n. The concept of an almost-almost F-irregular graph is introduced, on the basis of which a sufficient condition for the existence of an infinite number of F-irregular graphs is found for each graph F from the specified class. It is proved that for any biconnected graph F, the minimum of whose vertex degrees is 2, there are infinitely many F-irregular graphs.

Author Biographies

Tatiana S. Dovzhenok, Secondary school No. 30 of Gomel, 6 Piaсdziasiat gadow BSSR Street, Gomiel 246032, Belarus

PhD (physics and mathematics); teacher

Artem V. Filuta, Secondary school No. 30 of Gomel, 6 Piaсdziasiat gadow BSSR Street, Gomiel 246032, Belarus

student at the 11th grade

Nastassia E. Chuhai, Secondary school No. 30 of Gomel, 6 Piaсdziasiat gadow BSSR Street, Gomiel 246032, Belarus

student at the 11th grade

References

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Published
2024-07-15
Keywords: F-degree of a vertex, F-irregular graph, biconnected graph, (K3, K2)-consistent graph, almost-almost F-irregular graph, strong hypothesis about F-irregular graphs
Supporting Agencies The authors express their deep gratitude to the reviewer for his valuable comments on the article.
How to Cite
Dovzhenok, T. S., Filuta, A. V., & Chuhai, N. E. (2024). On some results of the study of F-irregular graphs in the class of  biconnected graphs F. Journal of the Belarusian State University. Mathematics and Informatics, 2, 54-64. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/5773
Issue
No 2 (2024): Journal of the Belarusian State University. Mathematics and Informatics
Section
Discrete Mathematics and Mathematical Cybernetics

Copyright (c) 2024 Journal of the Belarusian State University. Mathematics and Informatics

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