Bounding the first Zagreb index of a unicyclic graph in term of its repetition number

Wang, Maoqun; Liu, Ruhua

doi:10.22108/toc.2026.146502.2321

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	Bounding the first Zagreb index of a unicyclic graph in term of its repetition number
Transactions on Combinatorics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 03 آبان 1405 اصل مقاله (627.03 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2026.146502.2321
نویسندگان
Maoqun Wang^* ؛ Ruhua Liu
School of Mathematics and Information Sciences, Yantai University, Yantai, P.R. China
چکیده
The first Zagreb index $M_{1}$ is equal to the sum of the squares of the degrees of the vertices. The repetition number of a graph is the maximum multiplicity in the list of its vertex degrees. In this paper, we lower and upper bound the first Zagreb index of a unicyclic graph by expressions depending solely on their repetition number and give degree sequence for these graphs with the largest and smallest first Zagreb indices, respectively.
کلیدواژه‌ها
first Zagreb index؛ repetition number؛ unicyclic graph؛ degree sequence

مراجع
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Bounding the first Zagreb index of a unicyclic graph in term of its repetition number