Abstract:

 The relation between  cyclic edgeconnectivity and  cyclic connectivity of a 3regular connected graph G is studied. It is proved that the cyclic edgeconnectivity of G is equal to its cyclic connectivity. Further, the relation between the cyclic connectivity and the cyclic vertexconnectivity of G is discussed. It is shown that if the vertex number of G is more than 6 times  its cyclic connectivity, then  its cyclic connectivity  is equal to its cyclic vertexconnectivity.

Key words: 3regular connected graph, cyclic edgeconnectivity, cyclic connectivity, cyclic vertexconnectivity