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Nicely graceful labellings of tadpoles | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 13 اردیبهشت 1405 اصل مقاله (535.68 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30511.2509 | ||
| نویسندگان | ||
| I N. Suparta1؛ M. Baca2؛ M. Demange* 3؛ A. Semaničová-Feňovčíková4؛ N.L.D. Sintiari5 | ||
| 1Department of Mathematics, Universitas Pendidikan Ganesha, Bali, Indonesia | ||
| 2Department of Applied Mathematics and Informatics, Technical University of Koˇsice, Slovak | ||
| 3Department of Mathematical Science, RMIT University, Melbourne, Australia | ||
| 4Department of Applied Mathematics and Informatics, Technical University of Košice, Slovak | ||
| 5Department of Informatics, Universitas Pendidikan Ganesha, Bali, Indonesia | ||
| چکیده | ||
| A vertex-labelling $f:V\to \{0,1,\ldots, |E|\}$ for a finite undirected simple graph $G(V, E)$ is called graceful if $f$ is injective and satisfies the additional property that $\{|f(u)-f(v)|: \text{for every edge} uv\in E\}=\{1,2,\ldots,|E|\}$, where $|E|$ is the number of edges in $G$. Let $M$ be a maximum matching in $G$ and let $f$ also satisfy the property that $f(u)+f(v)=W$ for every $uv\in M$, where $W$ is a constant; then the labelling $f$ is called nicely graceful. Furthermore, if $M$ is a perfect matching in $G$, then $f$ is said to be strongly graceful. In this paper, we investigate nicely and strongly graceful labellings of cycles and tadpoles that are obtained from a cycle by attaching a path to a vertex of the cycle. This leads to a complete characterisation of nicely graceful cycles and strongly graceful tadpoles. | ||
| کلیدواژهها | ||
| graph labelling؛ graceful labelling؛ strongly/nicely graceful؛ tadpole graphs | ||
| مراجع | ||
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