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Unicyclic graphs with maximum Randić indices | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 13، دوره 8، شماره 1، خرداد 2023، صفحه 161-172 اصل مقاله (424.74 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.27230.1216 | ||
| نویسندگان | ||
| Roslan Hasni* 1؛ Nor Hafizah Md Husin2؛ Zhibin Du3 | ||
| 1UMT, Malaysia | ||
| 2Universiti Pendidikan Sultan Idris | ||
| 3School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China | ||
| چکیده | ||
| The Randi'c index $R(G)$ of a graph $G$ is the sum of the weights $(d_u d_v)^{-\frac{1}{2}}$ of all edges $uv$ in $G$, where $d_u$ denotes the degree of vertex $u$. Du and Zhou [On Randi'c indices of trees, unicyclic graphs, and bicyclic graphs, Int. J. Quantum Chem. 111 (2011), 2760--2770] determined the $n$-vertex unicyclic graphs with the third for $n\ge 5$, the fourth for $n\ge 7$ and the fifth for $n\ge 8$ maximum Randi'c indices. Recently, Li et al. [The Randi{' c} indices of trees, unicyclic graphs and bicyclic graphs, Ars Combin. 127 (2016), 409--419] obtained the $n$-vertex unicyclic graphs with the sixth and the seventh for $n\ge 9$ and the eighth for $n\ge 10$ maximum Randi'c indices. In this paper, we characterize the $n$-vertex unicyclic graphs with the ninth, the tenth, the eleventh, the twelfth and the thirteenth maximum Randi'c values. | ||
| کلیدواژهها | ||
| Randi' {c} index؛ Maximum values؛ Unicyclic graphs؛ Ordering | ||
| مراجع | ||
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