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Gutman index‎, ‎edge-Wiener index and edge-connectivity

فصلنامه معادلات در ترکیبات، دوره: 9، شماره: 4
Year: 1399
COI: JR_COMB-9-4_005
Language: EnglishView: 62
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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


‎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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