The chromatic equivalence class of graph B n - 6 , 1 , 2 ¯

Jianfeng Wang; Qiongxiang Huang; Chengfu Ye; Ruying Liu

Discussiones Mathematicae Graph Theory (2008)

  • Volume: 28, Issue: 2, page 189-218
  • ISSN: 2083-5892

Abstract

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By h(G,x) and P(G,λ) we denote the adjoint polynomial and the chromatic polynomial of graph G, respectively. A new invariant of graph G, which is the fourth character R₄(G), is given in this paper. Using the properties of the adjoint polynomials, the adjoint equivalence class of graph B n - 6 , 1 , 2 is determined, which can be regarded as the continuance of the paper written by Wang et al. [J. Wang, R. Liu, C. Ye and Q. Huang, A complete solution to the chromatic equivalence class of graph B n - 7 , 1 , 3 ¯ , Discrete Math. (2007), doi: 10.1016/j.disc.2007.07.030]. According to the relations between h(G,x) and P(G,λ), we also simultaneously determine the chromatic equivalence class of B n - 6 , 1 , 2 ¯ that is the complement of B n - 6 , 1 , 2 .

How to cite

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Jianfeng Wang, et al. "The chromatic equivalence class of graph $\overline{B_{n-6,1,2}}$." Discussiones Mathematicae Graph Theory 28.2 (2008): 189-218. <http://eudml.org/doc/270688>.

@article{JianfengWang2008,
abstract = {By h(G,x) and P(G,λ) we denote the adjoint polynomial and the chromatic polynomial of graph G, respectively. A new invariant of graph G, which is the fourth character R₄(G), is given in this paper. Using the properties of the adjoint polynomials, the adjoint equivalence class of graph $B_\{n-6,1,2\}$ is determined, which can be regarded as the continuance of the paper written by Wang et al. [J. Wang, R. Liu, C. Ye and Q. Huang, A complete solution to the chromatic equivalence class of graph $\overline\{B_\{n-7,1,3\}\}$, Discrete Math. (2007), doi: 10.1016/j.disc.2007.07.030]. According to the relations between h(G,x) and P(G,λ), we also simultaneously determine the chromatic equivalence class of $\overline\{B_\{n-6,1,2\}\}$ that is the complement of $B_\{n-6,1,2\}$.},
author = {Jianfeng Wang, Qiongxiang Huang, Chengfu Ye, Ruying Liu},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {chromatic equivalence class; adjoint polynomial; the smallest real root; the second smallest real root; the fourth character; samllest real root; second smallest real root; fourth character},
language = {eng},
number = {2},
pages = {189-218},
title = {The chromatic equivalence class of graph $\overline\{B_\{n-6,1,2\}\}$},
url = {http://eudml.org/doc/270688},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Jianfeng Wang
AU - Qiongxiang Huang
AU - Chengfu Ye
AU - Ruying Liu
TI - The chromatic equivalence class of graph $\overline{B_{n-6,1,2}}$
JO - Discussiones Mathematicae Graph Theory
PY - 2008
VL - 28
IS - 2
SP - 189
EP - 218
AB - By h(G,x) and P(G,λ) we denote the adjoint polynomial and the chromatic polynomial of graph G, respectively. A new invariant of graph G, which is the fourth character R₄(G), is given in this paper. Using the properties of the adjoint polynomials, the adjoint equivalence class of graph $B_{n-6,1,2}$ is determined, which can be regarded as the continuance of the paper written by Wang et al. [J. Wang, R. Liu, C. Ye and Q. Huang, A complete solution to the chromatic equivalence class of graph $\overline{B_{n-7,1,3}}$, Discrete Math. (2007), doi: 10.1016/j.disc.2007.07.030]. According to the relations between h(G,x) and P(G,λ), we also simultaneously determine the chromatic equivalence class of $\overline{B_{n-6,1,2}}$ that is the complement of $B_{n-6,1,2}$.
LA - eng
KW - chromatic equivalence class; adjoint polynomial; the smallest real root; the second smallest real root; the fourth character; samllest real root; second smallest real root; fourth character
UR - http://eudml.org/doc/270688
ER -

References

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