Superconnectivity of regular graphs with small diameter |
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| Authors: | Camino Balbuena Jianmin Tang |
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| Affiliation: | a Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Campus Nord, Edifici C2, C/ Jordi Girona 1 i 3, E-08034 Barcelona, Spain
b School of Electrical Engineering and Computer Science, The University of Newcastle, NSW2308, Australia |
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| Abstract: | A graph is superconnected, for short super-κ, 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-κ when g≥5 and a complete graph otherwise. |
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| Keywords: | Connectivity Superconnectivity Cutset Diameter Girth |
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