Connectivity of iterated line graphs

Authors:
Martin Knor;L'udovít Niepel
Affiliations:
Department of Mathematics, Slovak University of Technology, Faculty of Civil Engineering, Radlinského 11, 813 68 Bratislava, Slovak Republic;Department of Mathematics & Computer Science, Kuwait University, Faculty of Science, P.O. box 5969 Safat 13060, Kuwait
Venue:
Discrete Applied Mathematics
Year:
2003

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Abstract

In this paper we present lower bounds for the connectivity of the 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 connect ivity 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 the i-iterated line graph is true, then an analogous result is true for an arbitrary graph G if i is sufficiently large.