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.
Ifs= 2, thenQ(G) has an equitable quotient matrixB 17 = n−1 3n−4 1 5 0 1 0 7 with CP g17(x) =x 3 −(n+ 11)x 2 + (11n+ 24)x−30n+ 36
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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.