Codiameters of 3-Connected 3-Domination Critical Graphs Yaojun Chen, 1 * Feng Tian, 2 and Bing Wei 2 1 DEPARTMENT OF MATHEMATICS, NANJING UNIVERSITY NANJING 210093, CHINA E-mail: yaojunc@nju.edu.cn 2 INSTITUTE OF SYSTEMS SCIENCE ACADEMY OF MATHEMATICS AND SYSTEMS SCIENCES CHINESE ACADEMY OF SCIENCES BEIJING 100080, CHINA Received February 9, 2001; Revised August 23, 2001 DOI 10.1002/jgt.10015 Abstract: A graph G is 3-domination critical if its domination number  is 3 and the addition of any edge decreases  by 1. Let G be a 3-connected 3-domination critical graph of order n. In this paper, we show that there is a path of length at least n 2 between any two distinct vertices in G and the lower bound is sharp. ß 2002 John Wiley & Sons, Inc. J Graph Theory 39: 76–85, 2002 Keywords: codiameter; 3-connected; domination critical 1. INTRODUCTION In this paper, all graphs considered are connected, finite undirected graphs with- out loops and multiple edges. We follow [3] for notations. In [5], Sumner and —————————————————— Contract grant sponsor: NSFC. *Correspondence to: Yaojun Chen, Department of Mathematics, Nanjing University, Nanjing 210093, P.R. China. E-mail: yaojunc@nju.edu.cn ß 2002 John Wiley & Sons, Inc.