A proof of the universal fixer conjecture

Monika Rosicka

Abstract

For a given graph G = (V, E) and permutation pi : V -> V the prism pi G of G is defined as follows: V(pi G) = V(G) boolean OR V(G'), where G' is a copy of G, and E(pi G) = E(G) boolean OR E(G') boolean OR M-pi where M-pi = {uv' : u is an element of V (G), v = pi(u)} and v' denotes the copy of v in G'. The graph G is called a universal fixer if gamma(pi G) = gamma(G) for every permutation pi. The idea of universal fixers was introduced by Burger, Mynhardt and Weakley in 2004. In this work we prove that the edgeless graphs (K-n) over bar, are the only universal fixers.
 Author Monika Rosicka (FMPI / ITPA) Monika Rosicka,, - Institute of Theoretical Physics and Astrophysics Journal series Utilitas Mathematica, ISSN 0315-3681, (A 15 pkt) Issue year 2018 Vol 108 Pages 125-132 Publication size in sheets 0.5 Keywords in English prism graphs, domination Language en angielski Score (nominal) 15 Score Ministerial score = 15.0, ArticleFromJournalMinisterial score (2013-2016) = 15.0, ArticleFromJournal Publication indicators WoS Impact Factor: 2017 = 0.267 (2) - 2017=0.33 (5) Citation count*
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