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http://dx.doi.org/10.4134/BKMS.b200166

ON THE FIXING NUMBER OF FUNCTIGRAPHS  

Fazil, Muhammad (Centre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University Multan)
Javaid, Imran (Centre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University Multan)
Murtaza, Muhammad (Centre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University Multan)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.1, 2021 , pp. 171-181 More about this Journal
Abstract
The fixing number of a graph G is the smallest order of a subset S of its vertex set V (G) such that the stabilizer of S in G, ��S(G) is trivial. Let G1 and G2 be the disjoint copies of a graph G, and let g : V (G1) → V (G2) be a function. A functigraph FG 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 fixing number in passing from G to FG 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.
Keywords
Fixing set; fixing number; functigraph; complete graph; tree; join graph;
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