2016/10/28 by Hira Benish, Iqra Irshad, Benish, Hira +6
Computer Science · Engineering · Mathematics · #05C25 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems #math.CO #msc:05C25
paper · pdf · doi:10.48550/arxiv.1610.09232
19 Pages
openalex publication_date 2016/10/28 · arxiv created 2017/01/03 · arxiv updated 2017/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An automorphism group of a graph G is the set of all permutations of the vertex set of G that preserve adjacency and non adjacency of vertices in a graph. A fixing set of a graph G is a subset of vertices of G such that only the trivial automorphism fixes every vertex in S. Minimum cardinality of a fixing set of G is called the fixing number of G. In this article, we define a fractional version of the fixing number of a graph. We formulate the problem of finding the fixing number of a graph as an integer programming problem. It is shown that a relaxation of this problem leads to a linear programming problem and hence to a fractional version of the fixing number of a graph. We also characterize the graphs G with the fractional fixing number (|V(G)|)/(2) and the fractional fixing number of some families of graphs is also obtained.