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
be disjoint copies of a graph G
be a function. A functigraph
consists of the vertex set
and the edge set
. 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
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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MDPI and ACS Style
Fazil, M.; Murtaza, M.; Ullah, Z.; Ali, U.; Javaid, I. On the Distinguishing Number of Functigraphs. Symmetry 2018, 10, 332.
Fazil M, Murtaza M, Ullah Z, Ali U, Javaid I. On the Distinguishing Number of Functigraphs. Symmetry. 2018; 10(8):332.
Fazil, Muhammad; Murtaza, Muhammad; Ullah, Zafar; Ali, Usman; Javaid, Imran. 2018. "On the Distinguishing Number of Functigraphs." Symmetry 10, no. 8: 332.
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