Journal of University of Science and Technology of China ›› 2014, Vol. 44 ›› Issue (2): 96-100.DOI: 10.3969/j.issn.0253-2778.2014.02.003

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An upper bound for the Harary index of a connected graph and the corresponding extremal graph

LI Xiaoxin   

  1. 1.Department of Mathematics, Chizhou University, Chizhou 247000, China; 2.School of Mathematics and Computation Sciences, Anqing Normal University, Anqing 246133, China; 3.School of Mathematical Sciences, Anhui University, Hefei 230601, China
  • Received:2013-04-16 Revised:2013-09-06 Online:2014-02-28 Published:2014-02-28

Abstract: The Harary index of a graph is defined as the sum of reciprocals of distances between all pairs of vertices of the graph. The graph(s) with maximum Harary index among all graphs with given order and diameter was characterized, and an upper bound for the Harary index in terms of diameter was provided. In addition, the connected graphs of order n with the second maximum and the third maximum Harary indices were characterized, respectively.

Key words: graph, Harary index, diameter