- Tytuł:
- The Vertex-Rainbow Index of A Graph
- Autorzy:
- Mao, Yaping
- Powiązania:
- https://bibliotekanauki.pl/articles/31340818.pdf
- Data publikacji:
- 2016-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
vertex-coloring
connectivity
vertex-rainbow S-tree
vertex- rainbow index
Nordhaus-Gaddum type - Opis:
- The k-rainbow index rxk(G) of a connected graph G was introduced by Chartrand, Okamoto and Zhang in 2010. As a natural counterpart of the k-rainbow index, we introduce the concept of k-vertex-rainbow index rvxk(G) in this paper. In this paper, sharp upper and lower bounds of rvxk(G) are given for a connected graph G of order n, that is, 0 ≤ rvxk(G) ≤ n − 2. We obtain Nordhaus-Gaddum results for 3-vertex-rainbow index of a graph G of order n, and show that rvx3(G) + rvx3(Ḡ) = 4 for n = 4 and 2 ≤ rvx3(G) + rvx3(Ḡ) ≤ n − 1 for n ≥ 5. Let t(n, k, ℓ) denote the minimal size of a connected graph G of order n with rvxk(G) ≤ ℓ, where 2 ≤ ℓ ≤ n − 2 and 2 ≤ k ≤ n. Upper and lower bounds on t(n, k, ℓ) are also obtained.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2016, 36, 3; 669-681
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł