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Gauci, John Baptist; Pisanski, Tomaž; Sciriha, Irene
Applicable analysis and discrete mathematics, 2023, Letnik: 17, Številka: 2Journal Article
In this paper the problem of the existence of regular nut graphs is addressed. A generalization of Fowler’s Construction which is a local enlargement applied to a vertex in a graph is introduced to generate nut graphs of higher order. Let N(ρ) denote the set of integers n such that there exists a regular nut graph of degree ρ and order n. It is proven that N(3) = {12} ∪ {2k : k ≥ 9} and that N(4) = {8, 10, 12} ∪ {n : n ≥ 14}. The problem of determining N(ρ) for ρ > 4 remains completely open.
