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Open AccessArticle

On the Distinguishing Number of Functigraphs

1
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Multan 60800, Pakistan
2
Department of Mathematics, University of Education Lahore, Campus Dera Ghazi Khan 32200, Pakistan
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(8), 332; https://doi.org/10.3390/sym10080332
Received: 3 July 2018 / Revised: 4 August 2018 / Accepted: 4 August 2018 / Published: 9 August 2018
(This article belongs to the Special Issue Symmetry in Graph Theory)
Let G 1 and G 2 be disjoint copies of a graph G and g : V ( G 1 ) V ( G 2 ) be a function. A functigraph F G consists of the vertex set V ( G 1 ) V ( G 2 ) and the edge set E ( G 1 ) E ( G 2 ) { u v : g ( u ) = v } . In this paper, we extend the study of distinguishing numbers of a graph to its functigraph. We discuss the behavior of 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. View Full-Text
Keywords: distinguishing number; functigraph; complete graph distinguishing number; functigraph; complete graph
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MDPI and ACS Style

Fazil, M.; Murtaza, M.; Ullah, Z.; Ali, U.; Javaid, I. On the Distinguishing Number of Functigraphs. Symmetry 2018, 10, 332.

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