On the Harary index of graph operations

Das K. C., Xu K., CANGÜL İ. N., ÇEVİK A. S., Graovac A.

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2013
  • Doi Number: 10.1186/1029-242x-2013-339
  • Journal Name: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: graph, Harary index, graph operations, WIENER INDEX, TOPOLOGICAL INDEXES, HYPER-WIENER, TREES
  • Bursa Uludag University Affiliated: Yes

Abstract

The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, expressions for the Harary indices of the join, corona product, Cartesian product, composition and disjunction of graphs are derived and the indices for some well-known graphs are evaluated. In derivations some terms appear which are similar to the Harary index and we name them the second and third Harary index.