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A Matrix Method for Chromatic Polynomials
Journal of Combinatorial Theory, Series B, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Biggs, Norman, Norman Biggs
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Chromatic Polynomials of 2-Edge-Coloured Graphs [PDF]
Electronic Journal of Combinatorics, 2020 Using the definition of colouring of $2$-edge-coloured graphs derived from 2-edge-coloured graph homomorphism, we extend the definition of chromatic polynomial to 2-edge-coloured graphs.
Iain Beaton +3 more
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Bivariate Chromatic Polynomials of Mixed Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 The bivariate chromatic polynomial $\chi_G(x,y)$ of a graph $G = (V, E)$, introduced by Dohmen-P\"{o}nitz-Tittmann (2003), counts all $x$-colorings of $G$ such that adjacent vertices get different colors if they are $\le y$. We extend this notion to
Matthias Beck, Sampada Kolhatkar
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Chromatic Schultz and Gutman Polynomials of Jahangir Graphs J2,m and J3,m
Journal of Applied Mathematics, 2023 Topological polynomial and indices based on the distance between the vertices of a connected graph are widely used in the chemistry to establish relation between the structure and the properties of molecules.
Ramy Shaheen +2 more
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A categorification of the chromatic symmetric polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The Stanley chromatic polynomial of a graph $G$ is a symmetric function generalization of the chromatic polynomial, and has interesting combinatorial properties.
Radmila Sazdanović, Martha Yip
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On the complexity of generalized chromatic polynomials [PDF]
Advances in Applied Mathematics, 2017 J. Makowsky and B. Zilber (2004) showed that many variations of graph colorings, called CP-colorings in the sequel, give rise to graph polynomials. This is true in particular for harmonious colorings, convex colorings, mcctmcct-colorings, and rainbow ...
A. Goodall +4 more
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Chromatic roots as algebraic integers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 A chromatic root is a zero of the chromatic polynomial of a graph. At a Newton Institute workshop on Combinatorics and Statistical Mechanics in 2008, two conjectures were proposed on the subject of which algebraic integers can be chromatic roots, known ...
Adam Bohn
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CHROMATIC POLYNOMIALS AND BIALGEBRAS OF GRAPHS [PDF]
International Electronic Journal of Algebra, 2016 The chromatic polynomial is characterized as the unique polynomial invariant of graphs, compatible with two interacting bialgebras structures: the first coproduct is given by partitions of vertices into two parts, the second one by a contraction ...
L. Foissy
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Simultaneous quantification of longitudinal and transverse ocular chromatic aberrations with Hartmann–Shack wavefront sensor [PDF]
Journal of Innovative Optical Health Sciences, 2018 A simple method to objectively and simultaneously measure eye’s longitudinal and transverse chromatic aberrations was proposed. A dual-wavelength wavefront measurement system using two Hartmann–Shack wavefront sensors was developed. The wavefronts of the
Yangchun Deng +3 more
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The Amazing Chromatic Polynomial [PDF]
The Mathematical Intelligencer, 2022 17 pages, 8 ...
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