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PreprintCC BY 4.0arXiv

Generalized Chromatic Polynomials of Cycles and uni-cyclic Graphs

  • Dipnit Biswas
  • R. Venkatesh
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Abstract

In \cite{R81}, Read obtained an explicit formula for the generalized chromatic polynomials of cycle graphs using the classical deletion-contraction principle. In this paper, we take a linear-algebraic approach and present a new proof of Read's formula by realizing the generalized chromatic polynomials of cycle graphs as traces of certain linear operators. As an application of this approach, we also derive explicit formulas for the generalized chromatic polynomials of uni-cyclic graphs.

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Cite

BibTeXRIS
BibTeX
@misc{biswas2026generalized,
  title = {{Generalized Chromatic Polynomials of Cycles and uni-cyclic Graphs}},
  author = {Dipnit Biswas and R. Venkatesh},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07568},
  eprint = {2611.07568},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07568},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Generalized Chromatic Polynomials of Cycles and uni-cyclic Graphs
AU  - Dipnit Biswas
AU  - R. Venkatesh
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.07568
UR  - https://arxiv.org/abs/2611.07568
AB  - In \cite{R81}, Read obtained an explicit formula for the generalized chromatic polynomials of cycle graphs using the classical deletion-contraction principle. In this paper, we take a linear-algebraic approach and present a new proof of Read's formula by realizing the generalized chromatic polynomials of cycle graphs as traces of certain linear operators. As an application of this approach, we also derive explicit formulas for the generalized chromatic polynomials of uni-cyclic graphs.
ER  -