Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: vertex-coloring

Sortuj według:

Ogranicz wyniki do:

The Vertex-Rainbow Index of A Graph

100%

Mao Y.

Discussiones Mathematicae Graph Theory

2016

tom 36

nr 3

669-681

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Mao Y.

1 2016

Wyniki wyszukiwania

The Vertex-Rainbow Index of A Graph