Abstract
Hie line persistence of a graph G, ρ1 (G) is the minimum number of lines which must be removed to increase the diameter of G. In Ref.[7] (J. Shanghai Univ., 2003,7(4):352–357), we gave a characterization of graphs of diameter five wilh ρ1(G)⩾2. In this paper we will show that each of the 8 special graphs Xi(i=1,2,3,4,5,6,7,8) listed in condition (2) of Theorem 1 in Ref.[7] can not be deleted. Therefore the results we obtained in Ref.[7] can not in general be improved.
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