On the Distinguishing Number of Functigraphs

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 09 Aug 2018 English Publisher:MDPI AGJournal:Symmetry, volume 10, page 332 (eissn: 2073-8994,

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Authors: Muhammad Fazil; Muhammad Murtaza; Zafar Ullah; Usman Ali 0008; Imran Javaid;

doi: 10.3390/sym10080332

On the Distinguishing Number of Functigraphs

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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.

Related Organizations

Bahauddin Zakariya University
Pakistan
University of Okara
Pakistan

Keywords

Coloring of graphs and hypergraphs, complete graph, distinguishing number, functigraph

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