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 diam(G) 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 k−1≤hc(G)≤max{diam(G),k−1} . 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.
Original language | American English |
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Journal | Discrete Mathematics |
Volume | 309 |
Issue number | 14 |
DOIs | |
State | Published - Jul 2009 |
Keywords
- Connectivity
- Diameter
- Hamilton-connected index
- Iterated line graph
- Maximum degree
Disciplines
- Computer Sciences
- Mathematics