| A Complete Solution to the Chromatic Equivalence Class of Graph $\overline{B_{n-8,1,4}}$ |
| Received:October 14, 2010 Revised:January 13, 2011 |
| Key Words:
chromatic equivalence class adjoint polynomial the smallest real root the fourth character.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11161037) and the Science Found of Qinghai Province (Grant No.2011-z-907). |
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| Abstract: |
| Two graphs are defined to be adjointly equivalent if and only if their complements are chromatically equivalent. Using the properties of the adjoint polynomials and the fourth character $R_4(G)$, the adjoint equivalence class of graph $B_{n-8,1,4}$ is determined. According to the relations between adjoint polynomial and chromatic polynomial, we also simultaneously determine the chromatic equivalence class of $\overline{B_{n-8,1,4}}$ that is the complement of $B_{n-8,1,4}$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2012.03.001 |
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