Maximally edge-connected and vertex-connected graphs and digraphs: A survey |
| |
Authors: | Angelika Hellwig |
| |
Institution: | a Institut für Medizinische Statistik, Universitätsklinikum der RWTH Aachen, Pauwelsstraße 30, 52074 Aachen, Germany b Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen, Germany |
| |
Abstract: | Let D be a graph or a digraph. If δ(D) is the minimum degree, λ(D) the edge-connectivity and κ(D) the vertex-connectivity, then κ(D)?λ(D)?δ(D) is a well-known basic relationship between these parameters. The graph or digraph D is called maximally edge-connected if λ(D)=δ(D) and maximally vertex-connected if κ(D)=δ(D). In this survey we mainly present sufficient conditions for graphs and digraphs to be maximally edge-connected as well as maximally vertex-connected. We also discuss the concept of conditional or restricted edge-connectivity and vertex-connectivity, respectively. |
| |
Keywords: | Connectivity Edge-connectivity Vertex-connectivity Restricted connectivity Conditional connectivity Super-edge-connectivity Local-edge-connectivity Minimum degree Degree sequence Diameter Girth Clique number Line graph |
本文献已被 ScienceDirect 等数据库收录! |
|