A note on cycle spectra of line graphs

We show that line graphs G = L ( H ) with σ 2 ( G ) ≥ 7 contain cycles of all lengths k , 2 rad ( H ) + 1 ≤ k ≤ c ( G ) . This implies that every line graph of such a graph with 2 rad ( H ) ≥ Δ ( H ) is subpancyclic, improving a recent result of Xiong and Li. The bound on σ 2 ( G ) is best possible.