On the Distinguishing Number of Functigraphs

Symmetry

Muhammad Fazil¹  Muhammad Murtaza¹  Usman Ali¹  Imran Javaid¹  Zafar Ullah² 

[1] 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;

关键词: distinguishing number;    functigraph;    complete graph;   

DOI  :  10.3390/sym10080332

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown