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On some topological indices of Mycielskian graph and its complement | ||
Communications in Combinatorics and Optimization | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 13 فروردین 1404 اصل مقاله (563.05 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2025.30287.2400 | ||
نویسنده | ||
K. Vinothkumar* | ||
Department of Mathematics (H&S), Malla Reddy (MR) Deemed to be University, Medchal-Malkajgiri, Hyderabad, Telangana-500 100, India | ||
چکیده | ||
In this paper, we obtain a formula for the Harary index and hyper-Wiener index of Mycielskian of $G$, $\mu(G)$, and complement of $\mu(G)$. More precisely, we determine a formula for the hyper-Wiener index of $\mu(G)$ in terms of Zagreb indices of $G$ if the girth of $G$ is greater than $6$ and we deduce the result in [M. Azari in Discrete Math. Algorithms and Appl. 09 (2017) 1750022]. In addition, we find a formula for the vertex Padmakar-Ivan index of $\mu(G)$ if the girth of $G$ is greater than 7 and the complement of $\mu(G)$. | ||
کلیدواژهها | ||
Mycielskian of a graph؛ vertex Padmakar-Ivan index؛ Harary index؛ hyper-Wiener index | ||
مراجع | ||
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