대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제58권1호
  • /
  • Pages.171-181
  • /
  • 2021
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2020.02.21
  • 심사 : 2020.11.02
  • 발행 : 2021.01.31
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초록

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.

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