A proof of the universal fixer conjecture - Rosicka, Monika (Utilitas Mathematica, 2018)
For a given graph G = (V, E) and permutation π: V → V the prism πG of G is denned as follows: V(πG) = V(G) ∪ V(G'), where G' is a copy of G, and E(πG) = E(G)∪E(G')∪Mπ, where Mπ = uv': u ∈ V(G), v = π(u) and v' denotes the copy of v in G'. The graph G is called a universal fixer if λ(πG) = π(G) for every permutation π. The idea of universal fixers was introduced by Burger, Mynhardt and Weakley in 2004. In this work we prove that the edgeless graphs Kn are the only universal fixers. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.