paper

On the Distinguishing number of Functigraphs

arXiv:1612.00971

Abstract

Let $G_{1}$ and $G_{2}$ be disjoint copies of a graph $G$ , and let $g : V (G_{1}) \to V (G_{2})$ 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.

10 pages, 1 figure. arXiv admin note: text overlap with arXiv:1611.03346