Super connectivity of line graphs

The super connectivity κ′ and the super edge-connectivity λ′ are more refined network reliability indices than connectivity κ and edge-connectivity λ. This paper shows that for a connected graph G with order at least four rather than a star and its line graph L(G), κ′(L(G))=λ′(G) if and only if G is not super-λ′. 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 κ(L(G))=λ′(G). Furthermore, the authors show that the line graph of a super-λ′ graph is super-λ if the minimum degree is at least three.