%0 Journal Article
%T Chromatically Unique Bipartite Graphs With Certain 3-independent Partition Numbers
%A Roslan Hasni
%A Y.H. Peng
%J Matematika
%D 2006
%I Universiti Teknologi Malaysia
%X For integers p, q, s with p ¡Ý q ¡Ý 2 and s ¡Ý 0, let K2-s (p, q) denote the set of 2-connected bipartite graphs which can be obtained from Kp,q by deleting a set of s edges. In this paper, we prove that for any graph G   K2-s (p, q) with p ¡Ý q ¡Ý 3 and 1 ¡Ü s ¡Ü q-1, if the number of 3-independent partitions of G is 2p-1 + 2q-1 + s + 3, then G is chromatically unique. This result extends the similar theorem by Dong et al. (Discrete Math. vol. 224 (2000) 107-124).
%K Chromatic polynomial
%K chromatically equivalence
%K chromatically unique.
%U http://www.fs.utm.my/matematika/images/stories/matematika/20062228.pdf