Connectivity of iterated line graphs |
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Authors: | Yehong Shao |
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Institution: | Arts and Science, Ohio University Southern, Ironton, OH 45638, United States |
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Abstract: | Let k≥0 be an integer and Lk(G) be the kth iterated line graph of a graph G. Niepel and Knor proved that if G is a 4-connected graph, then κ(L2(G))≥4δ(G)−6. We show that the connectivity of G can be relaxed. In fact, we prove in this note that if G is an essentially 4-edge-connected and 3-connected graph, then κ(L2(G))≥4δ(G)−6. Similar bounds are obtained for essentially 4-edge-connected and 2-connected (1-connected) graphs. |
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Keywords: | Connectivity Essential edge connectivity Iterated line graph |
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