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On the Distinguishing number of Functigraphs

Authors :
Fazil, Muhammad
Mutaza, Muhammad
Ali, Usman
Javaid, Imran
Publication Year :
2016

Abstract

Let $G_{1}$ and $G_{2}$ be disjoint copies of a graph $G$, and let $g:V(G_{1})\rightarrow V(G_{2})$ be a function. A functigraph $F_{G}$ consists of the vertex set $V(G_{1})\cup V(G_{2})$ and the edge set $E(G_{1})\cup E(G_{2})\cup \{uv:g(u)=v\}$. In this paper, we extend the study of the distinguishing number of a graph to its functigraph. We discuss the behavior of the distinguishing number in passing from $G$ to $F_{G}$ and find its sharp lower and upper bounds. We also discuss the distinguishing number of functigraphs of complete graphs and join graphs.<br />Comment: 10 pages, 1 figure. arXiv admin note: text overlap with arXiv:1611.03346

Subjects

Subjects :
Mathematics - Combinatorics
05C15

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1612.00971
Document Type :
Working Paper