The Fixing Number of Spanning Trees of a Graph
S. Eje, and Y. Fajardo-Lim (12-21)
Abstract
An automorphism is an isomorphism from the vertex set of a graph G to itself. The set of all automorphisms of G together with the operation of composition of functions is called the automorphism group of G, denoted by Aut(G). A 𝑓ixing 𝑠et is a set of vertices to be fixed in G such that the only automorphism possible for the remaining unfixed vertices of G is the identity map. The 𝑓ixing number of a graph, denoted by 𝑓ix(𝐺), is the order of the smallest fixing set. In this paper, we investigate the fixing number of the spanning trees of some special classes of graphs and a simple graph G in general.