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Symmetry 2018, 10(8), 332; https://doi.org/10.3390/sym10080332

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.
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)
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Abstract

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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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Fazil, M.; Murtaza, M.; Ullah, Z.; Ali, U.; Javaid, I. On the Distinguishing Number of Functigraphs. Symmetry 2018, 10, 332.

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