On the Maximum and Minimum Sizes of a Graph with Givenk-Connectivity

• Autorzy: Yuefang Sun
• Języki publikacji: EN

Abstrakty

EN

The concept of k-connectivity κk(G), introduced by Chartrand in 1984, is a generalization of the cut-version of the classical connectivity. For an integer k ≥ 2, the k-connectivity of a connected graph G with order n ≥ k is the smallest number of vertices whose removal from G produces a graph with at least k components or a graph with fewer than k vertices. In this paper, we get a sharp upper bound for the size of G with κk(G) = t, where 1 ≤ t ≤ n − k and k ≥ 3; moreover, the unique extremal graph is given. Based on this result, we get the exact values for the maximum size, denoted by g(n, k, t), of a connected graph G with order n and κk(G) = t. We also compute the exact values and bounds for another parameter f(n, k, t) which is defined as the minimum size of a connected graph G with order n and κk(G) = t, where 1 ≤ t ≤ n − k and k ≥ 3.

Słowa kluczowe

EN

k-connectivity; generalized connectivity; connectivity

Kategorie tematyczne

• 05C35: Extremal problems
• 05C40: Connectivity

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 37
• Numer: 3
• Strony: 623-632

Daty

wydano

2017-08-01

otrzymano

2016-01-19

poprawiono

2016-05-27

zaakceptowano

2016-06-01

online

2017-07-06

Twórcy

autor

Yuefang Sun

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Identyfikatory

DOI

10.7151/dmgt.1941