Graphs on n vertices with signless Laplacian index at or above a threshold depending on n contain a trebly chorded cycle unless they are two exceptional graphs.
Gould, Results and problems on chorded cycles: a survey, Graphs Comb
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Signless Laplacian index conditions for trebly chorded cycles in graphs with given order
Graphs on n vertices with signless Laplacian index at or above a threshold depending on n contain a trebly chorded cycle unless they are two exceptional graphs.