Geodesic
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, Tome 2 (2024), pp. 54-64

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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 $n\geq 8$ there exists a $K_{3}$-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.
Keywords: $F$-degree of a vertex; $F$-irregular graph; biconnected graph; $(K_{3}, K_{2})$ -consistent graph; almost-almost $F$-irregular graph; strong hypothesis about $F$-irregular graphs 
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     author = {T. S. Dovzhenok and A. V. Filuta and N. E. Chuhai},
     title = {On some results of the study of $F$-irregular graphs in the class of biconnected graphs $F$},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {54--64},
     publisher = {mathdoc},
     volume = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2024_2_a4/}
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T. S. Dovzhenok; A. V. Filuta; N. E. Chuhai. 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, Tome 2 (2024), pp. 54-64. http://geodesic.mathdoc.fr/item/BGUMI_2024_2_a4/