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Minimally locally 1-connected graphs

Published online by Cambridge University Press:  17 April 2009

K.H. Kulkarni
K.H. Kulkarni
Affiliation:
Department of Mathematics, Victoria Jubilee Technical Institute, Bombay, India.
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Abstract

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The local connectivity, νk(G), of a graph G is the minimum of the connectivities of neighbourhoods of the vertices of G. G is minimally locally n-connected if νk(G) = n and for every edge x of G, νk(G−x) = n − 1. A necessary and sufficient condition for a locally connected graph to be minimally locally 1-connected is given, and it is shown that for n ≥ 7, is minimally locally 1-connected.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 1 , August 1978 , pp. 77 - 80
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Behzad, Mehdi and Chartrand, Gary, Introduction to the theory of graphs (Allyn and Bacon, Boston, 1971).Google Scholar
[2]Chartrand, Gary and Pippert, Raymond E., “Locally connected graphs”, Časopis Pěst. Mat. 99 (1974), 158–163.CrossRefGoogle Scholar
[3]Kulkarni, K.H., “Some topics in graph theory” (PhD thesis, Karnatak University, Dharwar, 1976).Google Scholar
[4]Kulkarni, K.H., “A characterization of critically locally 1-connected graphs”, submitted.Google Scholar