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Some bipartite Hamilton decomposable graphs that are regular of degree δ ≡ 2 (mod 4) are shown to have Hamilton decomposable line graphs. One consequence is that every bipartite Hamilton decomposable graph G with connectivity κ(G) = 2 has a Hamilton decomposable line graph L(G).
In this paper the following results are proved: 1. Let be a path with vertices, where and . Let be a matching in . Then is hamiltonian-connected. 2. Let be a connected graph of order , and let be a matching in . Then is hamiltonian-connected.
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