A sequence is Thue or nonrepetitive if it does not contain a repetition of any length. We consider a generalization of this notion. A j-subsequence of a sequence S is a subsequence in which two consecutive terms are at indices of difference j in S. A k-Thue sequence is a sequence in which every j-subsequence, for 1 j k, is also Thue. It was conjectured that… (More)
In this note, we derive the lower bound on the sum for Wiener index of bipartite graph and its bipartite complement, as well as the lower and upper bounds on this sum for the Randić index and Zagreb indices. We also discuss the quality of these bounds.