Das, Kinkar C.Xu, KexiangCangul, Ismail NaciCevik, Ahmet SinanGraovac, Ante2020-03-262020-03-2620131029-242Xhttps://dx.doi.org/10.1186/1029-242X-2013-339https://hdl.handle.net/20.500.12395/29696The 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.en10.1186/1029-242X-2013-339info:eu-repo/semantics/openAccessgraphHarary indexgraph operationsArticleQ2WOS:000323663700001Q2