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Czech and Slovak Conference GRAPHS 2000
May 15-19, 2000
Matej Bel University in Banská Bystrica
Liptovský Trnovec, Slovakia

Organizers
Roman Nedela

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Connectivity of Iterated Line Graphs
by
M. Knor
Bratislava
Coauthors: L. Niepel (Safat)

We present lower bounds for the connectivity of i-iterated line graph Li(G) of a graph G. We prove that if G is a connected regular graph and i >= 5, then the connectivity of Li(G) is equal to the degree of Li(G), that is, the connectivity of Li(G) attains its theoretical maximum (we remark that the bound on i is best possible). Moreover, if a hypothesis on the growth of the minimum degree of i-iterated line graph is true, then an analogous result is true for arbitrary graph G if i is sufficiently large.

Supported by VEGA grant 1/6293/99 and by Kuwait University grant #SM 172.

Date received: May 26, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafd-15.