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.
Ifn= 10, thenq(G) = 11.0666<11.7474 =q(K + 1,1,n−2)
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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.