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Gutman index, edge-Wiener index and edge-connectivity | ||
| Transactions on Combinatorics | ||
| دوره 9، شماره 4، اسفند 2020، صفحه 231-242 اصل مقاله (245.79 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2020.124104.1749 | ||
| نویسندگان | ||
| Jaya Mazorodze1؛ Simon Mukwembi2؛ Tomas Vetrik* 3 | ||
| 1Department of Mathematics, University of Zimbabwe, P. O. Box MP 167, Mount Pleasant, Harare, Zimbabwe | ||
| 2School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa | ||
| 3Department of Mathematics and Applied Mathematics, University of the Free State, P. O. Box 339, Bloemfontein, 9300, South Africa | ||
| چکیده | ||
| 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 ${\rm Gut}(G) \le \frac{2^4 \cdot 3}{5^5 (\lambda+1)} n^5 + O(n^4)$ is asymptotically tight for $\lambda \ge 8$. We improve this result considerably for $\lambda \le 7$ by presenting asymptotically tight upper bounds on ${\rm Gut}(G)$ and $W_e (G)$ for $2 \le \lambda \le 7$. | ||
| کلیدواژه‌ها | ||
| topological index؛ distance؛ degree | ||
| مراجع | ||
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