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The connectivity of line-graphs

✍ Scribed by Gary Chartrand; M. James Stewart


Publisher
Springer
Year
1969
Tongue
English
Weight
286 KB
Volume
182
Category
Article
ISSN
0025-5831

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## Abstract Chartrand and Stewart have shown that the line graph of an __n__‐connected graph is itself __n__‐connected. This paper shows that for every pair of integers __m__ > __n__ > 1 there is a graph of point connectivity __n__ whose line graph has point connectivity __m__. The corresponding qu

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A well-known conjecture of Thomassen says that every 4-connected line graph is hamiltonian. In this paper we prove that every 7-connected line graph is hamiltonian-connected. For line graph, C. Thomassen [l] made the following conjecture. Conjecture. Every 4-connected line graph is hamiltonian.

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## Abstract Sharp lower bounds for the point connectivity and line connectivity of the line graph __L(G__) and the total graph __T(G__) of a graph __G__ are determined. The lower bounds are expressed in terms of the point connectivity __k__, line connectivity Ξ», and minimum degree Ξ΄ of __G.__ It is