More connections between the matching polynomial and the chromatic polynomial

More connections between the matching polynomial and the chromatic polynomial

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The connection between the matching polynomial and the chromatic polynomial for triangle-free graphs was revealed in the work of Farrell and Whitehead. We extend this result to all graph by mirroring the corresponding result of Godsil and Gutman for the acyclic polynomial and the characteristic poly...

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Main Authors: Beatriz Carely Luna-Olivera, Criel Merino, Marcelino Ramírez-Ibáñez
Format: Article
Language:English
Published: Taylor & Francis Group 2019-12-01
Series:AKCE International Journal of Graphs and Combinatorics
Online Access:http://www.sciencedirect.com/science/article/pii/S0972860017301226
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spelling doaj-a5f54c314203467cb32d04ccc36f5b5b2020-11-25T03:11:48ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002019-12-01163319323More connections between the matching polynomial and the chromatic polynomialBeatriz Carely Luna-Olivera0Criel Merino1Marcelino Ramírez-Ibáñez2Instituto de Agroingeniería, Universidad del Papaloapan, Av. Ferrocarril S/N Loma Bonita, 68400, Oaxaca, MexicoInstituto de Matemáticas, Universidad Nacional Autónoma de México, Área de la Investigación científica, Circuito Exterior, C.U., Coyoacán, 04510, México D.F., MexicoInstituto de Agroingeniería, Universidad del Papaloapan, Av. Ferrocarril S/N Loma Bonita, 68400, Oaxaca, Mexico; Corresponding author.The connection between the matching polynomial and the chromatic polynomial for triangle-free graphs was revealed in the work of Farrell and Whitehead. We extend this result to all graph by mirroring the corresponding result of Godsil and Gutman for the acyclic polynomial and the characteristic polynomial. We also reintroduce the clique polynomial of Farrell as an evaluation of the U-polynomial of Noble and Welsh, which also happens to contain the matching and chromatic polynomials. Keywords: Matching polynomial, Chromatic polynomial, F-polynomial, U-polynomialhttp://www.sciencedirect.com/science/article/pii/S0972860017301226
collection DOAJ
language English
format Article
sources DOAJ
author Beatriz Carely Luna-Olivera
Criel Merino
Marcelino Ramírez-Ibáñez
spellingShingle Beatriz Carely Luna-Olivera
Criel Merino
Marcelino Ramírez-Ibáñez
More connections between the matching polynomial and the chromatic polynomial
AKCE International Journal of Graphs and Combinatorics
author_facet Beatriz Carely Luna-Olivera
Criel Merino
Marcelino Ramírez-Ibáñez
author_sort Beatriz Carely Luna-Olivera
title More connections between the matching polynomial and the chromatic polynomial
title_short More connections between the matching polynomial and the chromatic polynomial
title_full More connections between the matching polynomial and the chromatic polynomial
title_fullStr More connections between the matching polynomial and the chromatic polynomial
title_full_unstemmed More connections between the matching polynomial and the chromatic polynomial
title_sort more connections between the matching polynomial and the chromatic polynomial
publisher Taylor & Francis Group
series AKCE International Journal of Graphs and Combinatorics
issn 0972-8600
publishDate 2019-12-01
description The connection between the matching polynomial and the chromatic polynomial for triangle-free graphs was revealed in the work of Farrell and Whitehead. We extend this result to all graph by mirroring the corresponding result of Godsil and Gutman for the acyclic polynomial and the characteristic polynomial. We also reintroduce the clique polynomial of Farrell as an evaluation of the U-polynomial of Noble and Welsh, which also happens to contain the matching and chromatic polynomials. Keywords: Matching polynomial, Chromatic polynomial, F-polynomial, U-polynomial
url http://www.sciencedirect.com/science/article/pii/S0972860017301226
work_keys_str_mv AT beatrizcarelylunaolivera moreconnectionsbetweenthematchingpolynomialandthechromaticpolynomial
AT crielmerino moreconnectionsbetweenthematchingpolynomialandthechromaticpolynomial
AT marcelinoramirezibanez moreconnectionsbetweenthematchingpolynomialandthechromaticpolynomial
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