| Autor: |
Saeid Alikhani, Samaneh Soltani |
| Jazyk: |
angličtina |
| Rok vydání: |
2019 |
| Předmět: |
|
| Zdroj: |
Mathematics Interdisciplinary Research, Vol 4, Iss 2, Pp 239-251 (2019) |
| Druh dokumentu: |
article |
| ISSN: |
2476-4965 |
| DOI: |
10.22052/mir.2020.133523.1102 |
| Popis: |
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 the 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 depends on the number of some induced subgraphs generated by some suitable partitions of V(G) and V(H). Let Gk be the k-th power of G with respect to the join product. We prove that if G is a connected graph of order n ≥ 2, then Gk has the distinguishing index 2, except D'(K2+K2)=3. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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