Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
623-632
Opis fizyczny
Daty
wydano
2017-08-01
otrzymano
2016-01-19
poprawiono
2016-05-27
zaakceptowano
2016-06-01
online
2017-07-06
Twórcy
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1941