Super connectivity of line graphs

  • Authors:

  • Jun-Ming Xu;Min Lü;Meijie Ma;Angelika Hellwig

  • Affiliations:

  • Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China;Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen, Germany

  • Venue:
  • Information Processing Letters
  • Year:
  • 2005

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Abstract

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