On Fixing number of Functigraphs

2016/11/10 by Muhammad Fazil, Fazil, Muhammad, Imran Javaid +3 · 1 citation
Computer Science · Mathematics · #05C25 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #math.CO #msc:05C25

paper · pdf · doi:10.48550/arxiv.1611.03346

10 pages, 1figure

arxiv created 2016/11/10 · openalex publication_date 2016/11/10 · arxiv updated 2016/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The fixing number of a graph G is the order of the smallest subset S of its vertex set V(G) such that stabilizer of S in G, Γ_S(G) is trivial. Let G₁ and G₂ be disjoint copies of a graph G, and let g:V(G₁)→ V(G₂) be a function. A functigraph F_G consists of the vertex set V(G₁)∪ V(G₂) and the edge set E(G₁)∪ E(G₂)∪ \uv:v=g(u)\. In this paper, we study the behavior of the fixing number in passing from G to F_G and find its sharp lower and upper bounds. We also study the fixing number of functigraphs of some well known families of graphs like complete graphs, trees and join graphs.

Cited by

• On the Distinguishing number of Functigraphs

Related

• On The Fixatic Number of Graphs
• On The Fixed Number of Graphs
• On the Fractional fixing number of graphs
• On fixing sets of composition and corona product of graphs
• On Zero Forcing Number of Functigraphs