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Hamilton-connected indices of graphs |
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| Authors: | Zhi-Hong Chen Liming Xiong Huiya Yan |
| Institution: | a Department of Mathematics, Butler University, Indianapolis, IN 46208, USA b Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA c Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, PR China d Department of Mathematics, Jiangxi Normal University, PR China e Department of Mathematics, Millersville University, Millersville, PA 17551, USA |
| Abstract: | Let G be an undirected graph that is neither a path nor a cycle. Clark and Wormald L.H. Clark, N.C. Wormald, Hamiltonian-like indices of graphs, ARS Combinatoria 15 (1983) 131-148] defined hc(G) to be the least integer m such that the iterated line graph Lm(G) is Hamilton-connected. Let  be the diameter of G and k be the length of a longest path whose internal vertices, if any, have degree 2 in G. In this paper, we show that  . We also show that κ3(G)≤hc(G)≤κ3(G)+2 where κ3(G) is the least integer m such that Lm(G) is 3-connected. Finally we prove that hc(G)≤|V(G)|−Δ(G)+1. These bounds are all sharp. |
| Keywords: | Hamilton-connected index Iterated line graph Diameter Maximum degree Connectivity |
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