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Diameter-girth sufficient conditions for optimal extraconnectivity in graphs

Author
Balbuena, C.; Cera, M.; Diánez, A.; García, P.; Marcote, F.
Type of activity
Journal article
Journal
Discrete mathematics
Date of publication
2008-08
Volume
308
Number
16
First page
3526
Last page
3536
DOI
https://doi.org/10.1016/j.disc.2007.07.012 Open in new window
URL
http://dx.doi.org/10.1016/j.disc.2007.07.012 Open in new window
Abstract
For a connected graph G, the r th extraconnectivity ¿r(G) is defined as the minimum cardinality of a cutset X such that all remaining components after the deletion of the vertices of X have at least r+1 vertices. The standard connectivity and superconnectivity correspond to ¿0(G) and ¿1(G), respectively. The minimum r-tree degree of G , denoted by ¿r(G), is the minimum cardinality of N(T) taken over all trees T¿G of order |V(T)|=r+1, N(T) being the set of vertices not in T that are neig...
Keywords
Connectivity, Cutset, Diameter, Girth, Superconnectivity
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications

Participants