supported by NSFC(10971255);the Key Project of Chinese Ministry of Education(208161);the Program for New Century Excellent Talents in University,and The Project-sponsored by SRF for ROCS,SEM
the removal of which separates two cycles.G is said to be cyclically separable if G has a cyclic edge-cut.For a cyclically separable graph G
the cyclic edge-connectivity cλ(G) is the minimum cardinality of all cyclic edge-cuts of G.The cyclic vertex-cut and the cyclic vertex-connectivity cκ(G) can be defined similarly.In this paper
we provide upper and lower bounds for cλ and cκ for the total graph T(G) of G.
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references
Bondy J A,Murty U S R.Graph Theory[M].New York:Springer,2008.
Plummer M D.On the cyclic connectivity of planar graphs[J].Lecture Notes in Math,1972,303:235-242.
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