A survey on the generalized connectivity of graphs

Xueliang Li; Yaping Mao

A survey on the generalized connectivity of graphs

Combinatorics 2015-09-01 v9 Discrete Mathematics

Authors: Xueliang Li , Yaping Mao

Abstract

The generalized $k$ -connectivity $\kappa_k(G)$ of a graph $G$ was introduced by Hager before 1985. As its a natural counterpart, we introduced the concept of generalized edge-connectivity $\lambda_k(G)$ , recently. In this paper we summarize the known results on the generalized connectivity and generalized edge-connectivity. After an introductory section, the paper is then divided into nine sections: the generalized (edge-)connectivity of some graph classes, algorithms and computational complexity, sharp bounds of $\kappa_k(G)$ and $\lambda_k(G)$ , graphs with large generalized (edge-)connectivity, Nordhaus-Gaddum-type results, graph operations, extremal problems, and some results for random graphs and multigraphs. It also contains some conjectures and open problems for further studies.

Keywords

generalized connectivity generalized edge-connectivity graph classes algorithms computational complexity bounds Nordhaus-Gaddum random graphs

Cite

@article{arxiv.1207.1838,
  title  = {A survey on the generalized connectivity of graphs},
  author = {Xueliang Li and Yaping Mao},
  journal= {arXiv preprint arXiv:1207.1838},
  year   = {2015}
}

Comments

51 pages. arXiv admin note: text overlap with arXiv:1303.3881 by other authors

A survey on the generalized connectivity of graphs

Abstract

Keywords

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