Super connectivity of line graphs
The super connectivity kappa' and the super edge-connectivity lambda' are more refined network reliability indices than connectivity K and edge-connectivity lambda. This paper shows that for a connected graph G with order at least four rather than a star and its line graph L(G), kappa'(L(G)) = lambda' (G) if and only if G is not super-lambda'. As a consequence, we obtain the result of Hellwig et al. [Note on the connectivity of line graphs, Inform. Process. Lett. 91 (2004) 7] that K(L(G)) = lambda' (G). Furthermore, the authors show that the line graph of a super-lambda' graph is super-lambda if the minimum degree is at least three. (c) 2005 Elsevier B.V. All rights reserved.
super connectivity line graphs super edge-connectivity super-lambda ' lambda '-connected combinatorial problems