Superconnectivity of regular graphs with small diameter

Authors:
Camino Balbuena;Jianmin Tang;Kim Marshall;Yuqing Lin
Affiliations:
Departament de Matemítica Aplicada III, Universitat Politècnica de Catalunya, Campus Nord, Edifici C2, C/ Jordi Girona 1 i 3, E-08034 Barcelona, Spain;School of Electrical Engineering and Computer Science, The University of Newcastle, NSW2308, Australia;School of Electrical Engineering and Computer Science, The University of Newcastle, NSW2308, Australia;School of Electrical Engineering and Computer Science, The University of Newcastle, NSW2308, Australia
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 3
Cited 3

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Abstract

A graph is superconnected, for short super-@k, if all minimum vertex-cuts consist of the vertices adjacent with one vertex. In this paper we prove for any r-regular graph of diameter D and odd girth g that if D@?g-2, then the graph is super-@k when g=5 and a complete graph otherwise.