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On linear combinations between Zagreb indices/coindices of a line graph | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 8، شماره 2، مهر 2023، صفحه 65-74 اصل مقاله (276.98 K) | ||
| نوع مقاله: Special Issue of JDMA in the Memory of Prof. Ali Reza Ashrafi | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2023.9871.1054 | ||
| نویسندگان | ||
| Stefan Stankov؛ Marjan Matejic؛ Igor Milovanovic* ؛ Emina Milovanovic | ||
| Faculty of Electronic Engineering, University of Nis, Nis, Serbia | ||
| تاریخ دریافت: 06 خرداد 1402، تاریخ بازنگری: 13 خرداد 1402، تاریخ پذیرش: 25 خرداد 1402 | ||
| چکیده | ||
| Let $G=(V,E)$, $V=\left\{ v_{1},v_{2},\ldots ,v_{n}\right\}$, be a simple graph of order $n$ and size $m$. Denote by $\Delta = d_1\ge d_2 \ge \cdots \ge d_n= \delta$, $d_i=d(v_i)$, and $\Delta_e=d(e_1)\ge d(e_2)\ge \cdots \ge d(e_m)=\delta_e$, sequences of vertex and edge degrees, respectively. The first reformulated Zagreb index (coindex) is defined as $\displaystyle EM_1(G)=\sum_{i=1}^m d(e_i)^2 = \sum_{e_i\sim e_j}(d(e_i)+d(e_j))$ $\Big(\displaystyle \overline{EM}_1(G) = \sum_{e_i\nsim e_j}(d(e_i)+d(e_j))\Big)$. We consider relationship between reformulated Zagreb indices/coindices and determine their bounds in terms of some basic graph parameters. | ||
| کلیدواژه‌ها | ||
| Topological indices؛ Zagreb indices؛ Line graph | ||
| مراجع | ||
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