- Tytuł:
- The Distinguishing Number and Distinguishing Index of the Lexicographic Product of Two Graphs
- Autorzy:
-
Alikhani, Saeid
Soltani, Samaneh - Powiązania:
- https://bibliotekanauki.pl/articles/31342273.pdf
- Data publikacji:
- 2018-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
distinguishing index
distinguishing number
lexicographic - Opis:
- The distinguishing number (index) D(G) (D′(G)) of a graph G is the least integer d such that G has a vertex labeling (edge labeling) with d labels that is preserved only by the trivial automorphism. The lexicographic product of two graphs G and H, G[H] can be obtained from G by substituting a copy Hu of H for every vertex u of G and then joining all vertices of Hu with all vertices of Hv if uv ∈ E(G). In this paper we obtain some sharp bounds for the distinguishing number and the distinguishing index of the lexicographic product of two graphs. As consequences, we prove that if G is a connected graph with Aut(G[G]) = Aut(G)[Aut(G)], then for every natural number k, D(G) ≤ D(Gk) ≤ D(G) + k − 1 and all lexicographic powers of G, Gk (k ≥ 2) can be distinguished by two edge labels, where Gk = G[G[. . . ]].
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2018, 38, 3; 853-865
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł