Author:
Das Kinkar C,Xu Kexiang,Cangul Ismail Naci,Cevik Ahmet Sinan,Graovac Ante
Abstract
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.
MSC:05C05, 05C07, 05C90.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference28 articles.
1. Ivanciuc O, Balaban TS, Balaban AT: Reciprocal distance matrix, related local vertex invariants and topological indices. J. Math. Chem. 1993, 12: 309–318. 10.1007/BF01164642
2. Plavšić D, Nikolić S, Trinajstić N, Mihalić Z: On the Harary index for the characterization of chemical graphs. J. Math. Chem. 1993, 12: 235–250. 10.1007/BF01164638
3. Das KC, Zhou B, Trinajstić N: Bounds on Harary index. J. Math. Chem. 2009, 46: 1369–1376. 10.1007/s10910-009-9520-x
4. Das KC, Xu K, Gutman I: On Zagreb and Harary indices. MATCH Commun. Math. Comput. Chem. 2013, 70(1):301–314.
5. Ilić A, Yu G, Feng L: The Harary index of trees. Util. Math. 2012, 87: 21–32.
Cited by
22 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Resistance distance and sharp bounds of two-mode electrical networks;Physica Scripta;2024-07-19
2. Harary and hyper-Wiener indices of some graph operations;Journal of Inequalities and Applications;2024-03-15
3. The Second Omega Index;Current Organic Synthesis;2023-12-14
4. On the Harary Index of Graphs with Given Dissociation Number;Match - Communications in Mathematical and in Computer Chemistry;2023-07
5. On general Sombor index of graphs;Asian-European Journal of Mathematics;2022-09-07