Distinguishing number and distinguishing index of neighbourhood corona of two graphs

Authors

  • Saeid Alikhani Yazd University
  • Samaneh Soltani Yazd University

DOI:

https://doi.org/10.11575/cdm.v14i1.62665

Keywords:

Distinguishing index, Distinguishing number, neighborhood corona.

Abstract

The distinguishing number (index) D(G)D(G) (D(G)) of a graph G is the least integer d such that G has an vertex labeling (edge labeling)  with d labels  that is preserved only by a trivial automorphism. The neighbourhood corona of two graphs G1 and G2 is denoted by  G1G2  and is the graph obtained by     taking one copy of G1 and  |V(G1)| copies of G2, and joining the neighbours of the ith vertex of G1 to every vertex in the ith copy of G2. In this paper we describe the automorphisms of the graph G1G2. Using results on  automorphisms, we study the distinguishing number and the distinguishing index of G1G2.  We obtain upper bounds for D(G1G2) and D(G1G2).

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Published

2019-12-26

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Section

Articles