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On Wiener and multiplicative Wiener indices of graphs.
- Source :
-
Discrete Applied Mathematics . Jun2016, Vol. 206, p9-14. 6p. - Publication Year :
- 2016
-
Abstract
- Let G be a connected graph of order n with m edges and diameter d . The Wiener index W ( G ) and the multiplicative Wiener index π ( G ) of the graph G are equal, respectively, to the sum and product of the distances between all pairs of vertices of G . We obtain a lower bound for the difference π ( G ) − W ( G ) of bipartite graphs. From it, we prove that π ( G ) > W ( G ) holds for all connected bipartite graphs, except P 2 , P 3 , and C 4 . We also establish sufficient conditions for the validity of π ( G ) > W ( G ) in the general case. Finally, a relation between W ( G ) , π ( G ) , n , m , and d is obtained. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0166218X
- Volume :
- 206
- Database :
- Academic Search Index
- Journal :
- Discrete Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 114873636
- Full Text :
- https://doi.org/10.1016/j.dam.2016.01.037