Proves that for a χ-chromatic graph the first ℓ1−1 distance Laplacian eigenvalues satisfy ∂^L_i(G) ≥ n + ℓ1 where ℓ1 is the largest color-class size, refining distribution and extremal results.
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Explicit spectra are determined for the A_alpha, adjacency, signless Laplacian, Laplacian, and distance matrices of the zero-divisor graph of Z_p[x]/(x^c), with Laplacian and distance eigenvalues proven to be integers.
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Extremal chromatic bounds for distance Laplacian eigenvalues
Proves that for a χ-chromatic graph the first ℓ1−1 distance Laplacian eigenvalues satisfy ∂^L_i(G) ≥ n + ℓ1 where ℓ1 is the largest color-class size, refining distribution and extremal results.
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Spectral Properties of Zero-Divisor Graphs of Truncated Polynomial Rings
Explicit spectra are determined for the A_alpha, adjacency, signless Laplacian, Laplacian, and distance matrices of the zero-divisor graph of Z_p[x]/(x^c), with Laplacian and distance eigenvalues proven to be integers.