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arXiv · 1612.00971

On the Distinguishing number of Functigraphs

Muhammad Fazil·Muhammad Mutaza·Usman Ali·Imran Javaid
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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.

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Muhammad Fazil, Muhammad Mutaza, Usman Ali, Imran Javaid. 2016-12-03. On the Distinguishing number of Functigraphs. https://arxiv.org/abs/1612.00971

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