2019/04/03 by Gauci, John Baptist, Pisanski, Tomaz, Sciriha, Irene · 2 citations
#05C50 #15A03 #15A18 #15B34 #15B99 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1904.02229
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.