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.
Then g′ 5(x) = 5x4 −(4n+ 64)x 3 + (51n+ 219)x 2 −(192n+ 56)x+ 200n−356, g′′ 5(x) = 20x3 −(12n+ 192)x 2 + (102n+ 438)x−192n−56, g(3) 5 (x) = 60∗x 2 −(24n+ 384)x+ 102n+ 438
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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.