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

Discussiones Mathematicae Graph Theory (2017)

- Volume: 37, Issue: 3, page 623-632
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topYuefang Sun. "On the Maximum and Minimum Sizes of a Graph with Givenk-Connectivity." Discussiones Mathematicae Graph Theory 37.3 (2017): 623-632. <http://eudml.org/doc/288543>.

@article{YuefangSun2017,

abstract = {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.},

author = {Yuefang Sun},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {k-connectivity; generalized connectivity; connectivity},

language = {eng},

number = {3},

pages = {623-632},

title = {On the Maximum and Minimum Sizes of a Graph with Givenk-Connectivity},

url = {http://eudml.org/doc/288543},

volume = {37},

year = {2017},

}

TY - JOUR

AU - Yuefang Sun

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

JO - Discussiones Mathematicae Graph Theory

PY - 2017

VL - 37

IS - 3

SP - 623

EP - 632

AB - 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.

LA - eng

KW - k-connectivity; generalized connectivity; connectivity

UR - http://eudml.org/doc/288543

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.