Author/Authors :
Mazorodze, Jaya Department of Mathematics - University of Zimbabwe, Mount Pleasant, Harare, Zimbabwe , Mukwembi, Simon School of Mathematics - University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa , Vetrik, Tomas Department of Mathematics and Applied Mathematics - University of the Free State, Bloemfontein, 9300, South Africa
Abstract :
We study the Gutman index Gut(G) and the edge-Wiener index We(G) of connected graphs G of given order n and edge-connectivity λ. We show that the bound Gut(G)≤24⋅355(λ+1)n5+O(n4) is asymptotically tight for λ≥8. We improve this result considerably for λ≤7 by presenting asymptotically tight upper bounds on Gut(G) and We(G) for 2≤λ≤7.
