In this paper, we first establish the very close link between stability of graphs, a concept first introduced by Marušič, Scapellato and Zagaglia Salvi and studied most notably by Surowski and Wilson, and two-fold automorphisms. The concept of two-fold isomorphisms, as far as we know, first appeared in Zelinka’s work on isotopies of digraphs and later studied formally by the authors with a greater emphasis on undirected graphs. We then turn our attention to the stability of graphs which have every edge on a triangle, but with the fresh outlook provided by TF-automorphisms. Amongst such graphs are strongly regular graphs with certain parameters. The advantages of this fresh outlook are highlighted when we ultimately present a method of constructing and generating unstable graphs with large diameter having every edge lying on a triangle. This was a rather surprising outcome.
@article{534,
title = {Unstable graphs: A fresh outlook via TF-automorphisms},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {9},
year = {2014},
doi = {10.26493/1855-3974.534.934},
language = {EN},
url = {http://dml.mathdoc.fr/item/534}
}
Lauri, Josef; Mizzi, Russell; Scapellato, Raffaele. Unstable graphs: A fresh outlook via TF-automorphisms. ARS MATHEMATICA CONTEMPORANEA, Tome 9 (2014) . doi : 10.26493/1855-3974.534.934. http://gdmltest.u-ga.fr/item/534/