Physical Sciences and Mathematics Commons^™

Beta Invariant And Chromatic Uniqueness Of Wheels, Sooyeon Lee, Haidong Wu

Faculty and Student Publications

A graph G is chromatically unique if its chromatic polynomial completely determines the graph. An n-spoked wheel, Wn, is shown to be chromatically unique when n ≥ 4 is even [S.-J. Xu and N.-Z. Li, The chromaticity of wheels, Discrete Math. 51 (1984) 207–212]. When n is odd, this problem is still open for n ≥ 15 since 1984, although it was shown by di erent researchers that the answer is no for n = 5, 7, yes for n = 3, 9, 11, 13, and unknown for other odd n. We use the beta invariant of matroids to prove …