Gutman index, edge-Wiener index and edge-connectivity
Publish place: Transactions on Combinatorics، Vol: 9، Issue: 4
Publish Year: 1399
نوع سند: مقاله ژورنالی
زبان: English
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JR_COMB-9-4_005
تاریخ نمایه سازی: 14 اردیبهشت 1400
Abstract:
We study the Gutman index ${\rm Gut}(G)$ and the edge-Wiener index $W_e (G)$ of connected graphs $G$ of given order $n$ and edge-connectivity $\lambda$. We show that the bound ${\rm Gut}(G) \le \frac{۲^۴ \cdot ۳}{۵^۵ (\lambda+۱)} n^۵ + O(n^۴)$ is asymptotically tight for $\lambda \ge ۸$. We improve this result considerably for $\lambda \le ۷$ by presenting asymptotically tight upper bounds on ${\rm Gut}(G)$ and $W_e (G)$ for $۲ \le \lambda \le ۷$.
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Authors
Jaya Mazorodze
Department of Mathematics, University of Zimbabwe, P. O. Box MP ۱۶۷, Mount Pleasant, Harare, Zimbabwe
Simon Mukwembi
School of Mathematics, University of the Witwatersrand, Private Bag ۳, Wits ۲۰۵۰, South Africa
Tomas Vetrik
Department of Mathematics and Applied Mathematics, University of the Free State, P. O. Box ۳۳۹, Bloemfontein, ۹۳۰۰, South Africa