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A new version of Zagreb index of circumcoronene series of benzenoid | ||
| Journal of Discrete Mathematics and Its Applications | ||
| مقاله 3، دوره 2، 1-2، شهریور 2012، صفحه 15-20 اصل مقاله (975.68 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jmns.2012.466 | ||
| نویسنده | ||
| Mohammad Farahani | ||
| Department of Mathematics, Iran University of Science and Technology (IUST), Narmak, Tehran 16844, Iran | ||
| تاریخ دریافت: 13 مهر 1390، تاریخ بازنگری: 20 دی 1390، تاریخ پذیرش: 15 دی 1390 | ||
| چکیده | ||
| Among topological indices, Zagreb indices are very important, very old and they have many useful properties in chemistry and specially in mathematics chemistry. First and second Zagreb indices have been introduced by Gutman and Trinajstić as $M_1(G)=\sum_{uv\in E}d_u+d_v$ and $M_1(G)=\sum_{uv\in E}d_ud_v$, where du denotes the degree of vertex u in G. Recently, we know new versions of Zagreb indices as $M_1^{*}(G)=\sum_{uv\in E}ecc(u)+ecc(v)$, $M_1^{**}(G)=\sum_{u\in V}ecc(u)^2$ and $M_2^{*}(G)=\sum_{uv\in E}ecc(u)ecc(v)$, where ecc(u) is the largest distance between u and any other vertex v of G. In this paper, we focus one of these new topological indices that we call fifth Zagreb index $M_2^*(G)=M_5(G)$ and we compute this index for a famous molecular graph Circumcoronene series of benzenoid Hk, k≥ 1. | ||
| کلیدواژه‌ها | ||
| First Zagreb index؛ second Zagreb index؛ Fifth Zagreb index؛ Circumcoronene series of benzenoid؛ Cut Method؛ Ring-cut Method | ||
| مراجع | ||
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3. M.R. Farahani, Computing Zagreb index, Zagreb Polynomial and some Connectivity index of Circumcoronene series, Submitted.
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10. M. Ghorbani and M.A. Hosseinzadeh, A New Version of Zagreb Indices, Filomat, 26(1) (2012), 93–100.
11. M.R. Farahani, Computing eccentricity connectivity polynomial of circumcoronene series of benzenoid Hk by Ring-cut Method, Submitted. | ||
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