2016/03/13 by Saeid Alikhani, Alikhani, Saeid, Samaneh Soltani +1
Computer Science · Materials Science · #Graph Labeling and Dimension Problems #Photochromic and Fluorescence Chemistry
paper · pdf · doi:10.48550/arxiv.1603.04005
The distinguishing number (index) 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. In this paper we study the distinguishing number and the distinguishing index of join of two graphs G and H, i.e., G+H. We prove that 0≤ D(G+H)-max\D(G),D(H)\≤ z, where z is depends of the number of some induced subgraphs generated by some suitable partitions of V(G) and V(H). Also, we prove that if G is a connected graph of order n ≥ 2, then D'(G+ ⋯ +G)=2, except D'(K2+K2)=3.