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3-connected line graphs of triangular graphs are panconnected and 1- Hamiltonian. (English) Zbl 0656.05045
A graph G is k-triangular if each edge lies in at least k triangles. G is k-Hamiltonian if G-U is Hamiltonian for every subset U of vertices with \(0\leq | U| \leq k.\)
It is shown that if G is a 1-triangular graph with at least 4 vertices, then the line graph L(G) is panconnected if and only if L(G) is 3- connected. The main tool in the proof is a characterization of line graphs by Harary and Nash-Williams.
In the case of a k-triangular graph, L(G) is k-Hamiltonian if and only if L(G) is \((k+2)\)-connected.
Reviewer: N.Quimpo

MSC:
05C45 Eulerian and Hamiltonian graphs
05C99 Graph theory
05C40 Connectivity
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