Existence of regular nut graphs and the fowler construction | Zendy

Baptist Gauci | Zendy; Tomaž Pisanski | Zendy; Irene Sciriha | Zendy

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Existence of regular nut graphs and the fowler construction

Author(s) -

Baptist Gauci,

Tomaž Pisanski,

Irene Sciriha

Publication year - 2020

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm190517028g

Subject(s) - mathematics , nut , combinatorics , vertex (graph theory) , graph , generalization , discrete mathematics , mathematical analysis , structural engineering , engineering

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 (?) denote the set of integers n such that there exists a regular nut graph of degree ? 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 (?) for ? > 4 remains completely open.

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