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Leech Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 3، دوره 9، شماره 2، شهریور 2024، صفحه 205-215 اصل مقاله (421.74 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.27735.1339 | ||
| نویسندگان | ||
| Seena Varghese* 1؛ Aparna Lakshmanan Savithri2؛ S. Arumugam3 | ||
| 1Department of Mathematics, Federal Institute of Science and Technology, Angamaly-683577, Ernakulam District, Kerala, India | ||
| 2Department of Mathematics, Cochin University of Science and Technology,Cochin-22, Kerala,India | ||
| 3National Centre for Advanced Research in Discrete Mathematics, Kalasalingam University Anand Nagar, Krishnankoil-626 126, Tamil Nadu, India | ||
| چکیده | ||
| Let $t_p(G)$ denote the number of paths in a graph $G$ and let $f:E\rightarrow \mathbb{Z}^+$ be an edge labeling of $G$. The weight of a path $P$ is the sum of the labels assigned to the edges of $P$. If the set of weights of the paths in $G$ is $\{1,2,3,\dots,t_p(G)\}$, then $f$ is called a Leech labeling of $G$ and a graph which admits a Leech labeling is called a Leech graph. In this paper, we prove that the complete bipartite graphs $K_{2,n}$ and $K_{3,n}$ are not Leech graphs and determine the maximum possible value that can be given to an edge in the Leech labeling of a cycle. | ||
| کلیدواژه‌ها | ||
| Leech labeling؛ Leech tree؛ Leech graph | ||
| مراجع | ||
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[10] S. Varghese, A. Lakshmanan S., and S. Arumugam, Two classes of non-Leech trees, Electron. J. Graph Theory Appl. 8 (2020), no. 1, 205–210. https://doi.org/10.5614/ejgta.2020.8.1.15
[11] S. Varghese, A. Lakshmanan S., and S. Arumugam, Leech index of a tree, J. Discrete Math. Sci. Crypt. 25 (2022), no. 8, 2237–2247. https://doi.org/10.1080/09720529.2020.1800217 [12] S. Varghese, A. Lakshmanan S., and S. Arumugam, Two extensions of Leech labeling to the class of all graphs, AKCE Int. J. Graphs Comb. 19 (2022), no. 2, 159–165. http://doi.org/10.1080/09728600.2022.2084354
[13] S. Varghese, A. Lakshmanan S., and S. Arumugam, Leech labeling problem on tristar, AIP Conf. Proc. 2649 (2023), no. 1, ID: 020007. https://doi.org/10.1063/5.0114834 | ||
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