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