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Symmetry 2018, 10(8), 332;

On the Distinguishing Number of Functigraphs

Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Multan 60800, Pakistan
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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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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Fazil, M.; Murtaza, M.; Ullah, Z.; Ali, U.; Javaid, I. On the Distinguishing Number of Functigraphs. Symmetry 2018, 10, 332.

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