The chromaticity of wheels with a missing spoke

In the previous paper, it was shown that the graph Un + 1 obtained from the wheel Wn + 1 by deleting a spoke is uniquely determined by its chromatic polynomial if n ⩾ 3 is odd. In this paper, we show that the result is also true for even n ⩾ 4 except when n = 6 in which case, the graph W given in the paper is the only graph having the same chromatic polynomial as that of U7. The relevant tool is the notion of nearly uniquely colorable graph.

[1]  Chong-Yun Chao,et al.  Chromatically unique graphs , 1979, Discret. Math..

[2]  E. J. Farrell,et al.  On chromatic coefficients , 1980, Discret. Math..

[3]  R. Read.  An introduction to chromatic polynomials , 1968 .

[4]  Chong-Yun Chao,et al.  On chromatic equivalence of graphs , 1978 .

[5]  Ronald C. Read.  A note on the chromatic uniqueness of W10 , 1988, Discret. Math..

[6]  Kee L. Teo,et al.  The search for chromatically unique graphs , 1990, Graphs Comb..

[7]  Lian-Chang Zhao,et al.  Cutpoints and the chromatic polynomial , 1984, J. Graph Theory.

[8]  Frank Harary,et al.  Graph Theory , 2016 .

[9]  Shaoji Xu,et al.  The chromaticity of wheels , 1984, Discret. Math..