On prime coprime graphs of certain finite groups

	On prime coprime graphs of certain finite groups
Communications in Combinatorics and Optimization
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 04 شهریور 1405
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2026.30921.2661
نویسندگان
Ravi Ranjan؛ Shubh N. Singh^*
Department of Mathematics, Central University of South Bihar, Gaya–824236, Bihar, India
چکیده
The prime coprime graph $\Theta(G)$ of a finite group $G$ is the graph whose vertex set is $G$ and any two distinct vertices are adjacent if the greatest common divisor of their orders is either $1$ or a prime. In this paper, we investigate Hamiltonicity, clique number, and vertex degree of $\Theta(G)$ for cyclic, dihedral, and dicyclic groups $G$. We establish that $\Theta(G)$ admits a $(k,1)$-partition for cyclic, dihedral, and dicyclic groups $G$ of specified orders.
کلیدواژه‌ها
Hamiltonian graph؛ clique number؛ H-join؛ (k؛ l)-partition

آمار تعداد مشاهده مقاله: 6

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