Open AccessExistence of regular nut graphs and the fowler construction
Author(s) -
John Baptist Gauci,
Tomaž Pisanski,
Irene Sciriha
Publication year - 2023
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) , generalization , graph , 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.