Orbit-counting polynomials for graphs and codes

DOI10.1016/j.disc.2007.07.108zbMath1133.05030OpenAlexW2130791336MaRDI QIDQ2470463

Peter J. Cameron, Jason D. Rudd, Bill Jackson

Publication date: 14 February 2008

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2007.07.108

zbMATH Keywords

weight enumeratorgroup actionchromatic polynomialTutte polynomialnowhere-zero flowsorbit-counting

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Coloring of graphs and hypergraphs (05C15)

Related Items

The number of nowhere-zero flows on graphs and signed graphs ⋮ The odd-valued chromatic polynomial of a signed graph ⋮ A note on counting flows in signed graphs ⋮ Enumeration of substitutional isomers with restrictive mutual positions of ligands. II. Counts with restrictions on (sub)symmetry ⋮ The cycle polynomial of a permutation group ⋮ Combinatorial Hopf algebras from representations of families of wreath products ⋮ Tutte polynomials for counting and classifying orbits

Cites Work

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• The number of nowhere-zero flows on graphs and signed graphs
• Hyperplane reconstruction of the Tutte polynomial of a geometric lattice
• A weighted graph polynomial from chromatic invariants of knots
• A symmetric function generalization of the chromatic polynomial of a graph
• Acyclic orientations of graphs
• Orbital Chromatic and Flow Roots
• Weight Enumeration and the Geometry of Linear Codes
• Cycle index, weight enumerator, and Tutte polynomial