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 P2, P3, and C4. 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
