Journal of Prime Research in Mathematics

# On some parameters related to fixing sets in graphs

Imran Javaid
Centre for advanced studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Pakistan.
Muhammad Fazil$$^1$$
Centre for advanced studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Pakistan.
Usman Ali
Centre for advanced studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Pakistan.
$$^{1}$$Corresponding Author: mfazil@bzu.edu.pk
The fixing number of a graph G is the smallest cardinality of a set of vertices $$F ⊆ V (G)$$ such that only the trivial automorphism of $$G$$ fixes every vertex in $$F$$. In this paper, we introduce and study three new fixing parameters: fixing share, fixing polynomial and fixing value.