394 KB34 KB200820252015Lauri, JosefMizzi, RussellScapellato, Raffaeleštevilka:1letnik:8str. 115-131COBISSID:17369433ISSN:1855-3966URN:URN:NBN:SI:doc-8UBLEHASenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneacanonical double coversdvoslojni avtomorfizmigrafigraphskanonični dvojni krovitwo-fold isomorphismsUnstable graphs: a fresh outlook via TF-automorphisms|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 outcomeV tem članku najprej vzpostavimo zelo tesno zvezo med stabilnostjo grafov, konceptom, ki so ga najprej vpeljali Marušič, Scapellato in Zagaglia Salvi in sta ga najbolj intenzivno študirala Surowski in Wilson, ter dvo-slojnimi avtomorfizmi. Koncept dvo-slojnega avtomorfizma, se je, kolikor nam je znano, najprej pojavil v delu Zelinke o izotopijah digrafov in so ga avtorji kasneje študirali z večjim poudarkom na neusmerjenih grafih. Nato se posvetimo stabilnosti grafov, ki imajo vsako povezavo na trikotniku, vendar s svežim pogledom, ki ga omogočajo TF-avtomorfizmi. Med takšnimi grafi so tudi krepko regularni grafi z določenimi parametri. Prednosti tega svežega pogleda pridejo do izraza pri nazadnje predstavljeni metodi konstruiranja in generiranja nestabilnih grafov z velikim premerom, v katerih vsaka povezava pripada nekemu trikotniku. To je bil precej presenetljiv rezultatTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije