Then g′ 1(x) = 4x3 −(3n+ 45)x 2 + (32n+ 116)x−80n+ 24, g′′ 1(x) = 12x2 −(6n+ 90)x+ 32n+ 116

Proof ofq(G 1)< q(K + 1,1,n−2): Note thatQ(G 1) has an equitable quotient matrixB 1 = n−2 4n−6 0 1 6 0 1 1 0 7 0 0 4 0 4 with CP g1(x) =x 4 −(n+ 15)x 3 + (16n+ 58)x 2 −(80n−24)x+ 1

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Signless Laplacian index conditions for trebly chorded cycles in graphs with given order

math.CO · 2026-04-17 · unverdicted · novelty 4.0

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.

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Signless Laplacian index conditions for trebly chorded cycles in graphs with given order math.CO · 2026-04-17 · unverdicted · none · ref 22
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′ 1(x) = 4x3 −(3n+ 45)x 2 + (32n+ 116)x−80n+ 24, g′′ 1(x) = 12x2 −(6n+ 90)x+ 32n+ 116

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