What question did this study set out to answer?

This study aims to analyze chromatic-root loci in prism-derived graph families using spectral expansions and transfer-matrix reductions.

July 15, 2026Symmetry0 citationsOpen Access

Chromatic Polynomials and Spectral Analysis of Prism-Derived Graph Families

Quartic Equimodular Curves and Spectral Reductions in Prism-Derived Chromatic Polynomials

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Randomized analysis reveals chromatic-root loci in graph families, suggesting significant spectral competition.

This study aims to analyze chromatic-root loci in prism-derived graph families using spectral expansions and transfer-matrix reductions.
Analyzed chromatic polynomials using finite transfer-matrix reductions.
Examined the antiprism family An and circulant family Cn(1,2) with respect to spectral branches.
Investigated the generalized Petersen family G(n,2) and its irreducible cubic equations.
Proved that the quartic equation is the equimodular accumulation locus for An with a node at z=3 separating dominance types.
Identified a nonfixed isolated accumulation point at B5=(3+5)/2 for An and its even subsequence Cn(1,2).
Demonstrated that for Cn(1,3), reduced-sector equimodular locus collapses to ℜ(z)=2, |ℑ(z)|≤2.

Lopez-Bonilla et al. (2026) studied this question.

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July 15, 2026Symmetry0 citationsOpen Access

Quartic Equimodular Curves and Spectral Reductions in Prism-Derived Chromatic Polynomials

View Full Paper

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Bookmark

Authors

Randomized analysis reveals chromatic-root loci in graph families, suggesting significant spectral competition.

This study aims to analyze chromatic-root loci in prism-derived graph families using spectral expansions and transfer-matrix reductions.
Analyzed chromatic polynomials using finite transfer-matrix reductions.
Examined the antiprism family An and circulant family Cn(1,2) with respect to spectral branches.
Investigated the generalized Petersen family G(n,2) and its irreducible cubic equations.
Proved that the quartic equation is the equimodular accumulation locus for An with a node at z=3 separating dominance types.
Identified a nonfixed isolated accumulation point at B5=(3+5)/2 for An and its even subsequence Cn(1,2).
Demonstrated that for Cn(1,3), reduced-sector equimodular locus collapses to ℜ(z)=2, |ℑ(z)|≤2.

Lopez-Bonilla et al. (2026) studied this question.

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