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Counting formulas for weakly labelled plane tree-like structures | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 10، شماره 3، آذر 2025، صفحه 243-261 اصل مقاله (286.96 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2025.11860.1123 | ||
| نویسندگان | ||
| Sylvester Arthur Abayo1؛ Isaac Owino Okoth* 2؛ Donnie Munyao Kasyoki3 | ||
| 1Department of Pure and Applied Mathematics, Maseno University, Maseno, Kenya | ||
| 2Department of Pure and Applied Mathematics, School of Mathematics, Statistics and Actuarial Science, Maseno University, Maseno, Kenya | ||
| 3Department of Pure and Applied Mathematics, Maseno University, Maseno, Kenya. | ||
| تاریخ دریافت: 26 اسفند 1403، تاریخ بازنگری: 21 فروردین 1404، تاریخ پذیرش: 01 اردیبهشت 1404 | ||
| چکیده | ||
| Block graphs have been enumerated by various authors. In this paper, plane tree-like structures in which the blocks are labelled with integers in the set {1,2,...,k} such that the labels of the blocks are non-decreasing from left to right are introduced. These tree-like structures are called weakly labelled k-plane tree-like structures herein. Using symbolic method, generating functions and application of Lagrange-B\"{u}rmann inversion, the structures are counted by number of vertices, blocks, occurrences of labels, root degree and label of the eldest/youngest block child of the root, number of leaves, forests and outdegree sequence. | ||
| کلیدواژه‌ها | ||
| block؛ degree؛ eldest block child؛ forest؛ outdegree sequence | ||
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آمار تعداد مشاهده مقاله: 95 تعداد دریافت فایل اصل مقاله: 98 |
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