On maximum Wiener index of trees and graphs with given radius

On maximum Wiener index of trees and graphs with given radius

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Article ID: iaor20172787
Volume: 34
Issue: 2
Start Page Number: 574
End Page Number: 587
Publication Date: Aug 2017
Journal: Journal of Combinatorial Optimization
Authors: ,
Keywords: combinatorial optimization, graphs, heuristics
Abstract:

Let G be a connected graph of order n. The long‐standing open and close problems in distance graph theory are: what is the Wiener index W(G) or average distance μ ( G ) equ1 among all graphs of order n with diameter d (radius r)? There are very few number of articles where were worked on the relationship between radius or diameter and Wiener index. In this paper, we give an upper bound on Wiener index of trees and graphs in terms of number of vertices n, radius r, and characterize the extremal graphs. Moreover, from this result we give an upper bound on μ ( G ) equ2 in terms of order and independence number of graph G. Also we present another upper bound on Wiener index of graphs in terms of number of vertices n, radius r and maximum degree Δ equ3 , and characterize the extremal graphs.

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