Wszystkie pola: distinguishing number - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Trees with Distinguishing Index Equal Distinguishing Number Plus One
Autorzy:: Alikhani, Saeid
Klavžar, Sandi
Lehner, Florian
Soltani, Samaneh
Powiązania:: https://bibliotekanauki.pl/articles/31804165.pdf
Data publikacji:: 2020-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: automorphism group
distinguishing index
distinguishing number
tree
unicyclic graph
Opis:: The distinguishing number (index) D(G) (D′ (G)) of a graph G is the least integer d such that G has an vertex (edge) labeling with d labels that is preserved only by the trivial automorphism. It is known that for every graph G we have D′ (G) ≤ D(G) + 1. In this note we characterize finite trees for which this inequality is sharp. We also show that if G is a connected unicyclic graph, then D′ (G) = D(G).
Źródło:: Discussiones Mathematicae Graph Theory; 2020, 40, 3; 875-884
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

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 H_u of H for every vertex u of G and then joining all vertices of H_u with all vertices of H_v 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(G^k) ≤ D(G) + k − 1 and all lexicographic powers of G, G^k (k ≥ 2) can be distinguished by two edge labels, where G^k = 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

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