On Harary index of graphs
The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. For a connected graph G=(V,E) and two nonadjacent vertices v sub(i and v) sub(j) in V(G) of G, recall that G+v sub(iv) sub(j) is the supergraph formed from G by adding an edge betwe...
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| Veröffentlicht in: | Discrete Applied Mathematics 2011-09, Vol.159 (15), p.1631-1640 |
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| creator | KEXIANG XU DAS, Kinkar Ch |
| description | The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. For a connected graph G=(V,E) and two nonadjacent vertices v sub(i and v) sub(j) in V(G) of G, recall that G+v sub(iv) sub(j) is the supergraph formed from G by adding an edge between vertices v sub(i and v) sub(j). Denote the Harary index of G and G+v sub(iv) sub(j) by H(G) and H(G+v sub(iv) sub(j)), respectively. We obtain lower and upper bounds on H(G+v sub(iv) sub(j))-H(G), and characterize the equality cases in those bounds. Finally, in this paper, we present some lower and upper bounds on the Harary index of graphs with different parameters, such as clique number and chromatic number, and characterize the extremal graphs at which the lower or upper bounds on the Harary index are attained. |
| doi_str_mv | 10.1016/j.dam.2011.06.003 |
| format | Article |
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| subjects | Algorithmics. Computability. Computer arithmetics Applied sciences Combinatorics Combinatorics. Ordered structures Computer science control theory systems Exact sciences and technology Graphs Information retrieval. Graph Mathematical analysis Mathematics Recall Sciences and techniques of general use Theoretical computing Upper bounds |
| title | On Harary index of graphs |
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