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On the Zagreb indices of graphs with given Roman domination number | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 11، دوره 8، شماره 1، خرداد 2023، صفحه 141-152 اصل مقاله (377.96 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.27439.1263 | ||
| نویسندگان | ||
| Ayu Ameliatul Shahilah Ahmad Jamri1؛ Roslan Hasni* 2؛ Sharifah Kartini Said Husain3 | ||
| 1MENGGABANG TELIPOT KUALA NERUS | ||
| 2Universiti Malaysia Terengganu(UMT), Malaysia | ||
| 3Universiti Putra Malaysia(UPM) | ||
| چکیده | ||
| Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. The two Zagreb indices $M_1=\sum_{v\in V(G)} d^2_G(v)$ and $M_2=\sum_{uv\in E(G)} d_G(u)d_G(v)$ are vertex degree based graph invariants that have been introduced in the 1970s and extensively studied ever since. {In this paper, we first give a lower bound on the first Zagreb index of trees with given Roman domination number and we characterize all extremal trees. Then we present upper bound for Zagreb indices of unicyclic and bicyclic graphs with given Roman domination number. | ||
| کلیدواژهها | ||
| Zagreb index؛ Roman domination number؛ tree | ||
| مراجع | ||
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