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.
19 Then g′ 2(x) = 5x4 −(4n+ 80)x 3 + (63n+ 399)x 2 −(320n+ 520)x+ 520n−452, g′′ 2(x) = 20x3 −(12n+ 240)x 2 + (126n+ 798)x−320n−520, g(3) 2 (x) = 60x2 −(24n+ 480)x+ 126n+ 798
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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.