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.
Abayo, S. Arthur , Okoth, I. Owino and Kasyoki, D. Munyao (2025). Counting formulas for weakly labelled plane tree-like structures. Journal of Discrete Mathematics and Its Applications, 10(3), 243-261. doi: 10.22061/jdma.2025.11860.1123
MLA
Abayo, S. Arthur, , Okoth, I. Owino, and Kasyoki, D. Munyao. "Counting formulas for weakly labelled plane tree-like structures", Journal of Discrete Mathematics and Its Applications, 10, 3, 2025, 243-261. doi: 10.22061/jdma.2025.11860.1123
HARVARD
Abayo, S. Arthur, Okoth, I. Owino, Kasyoki, D. Munyao (2025). 'Counting formulas for weakly labelled plane tree-like structures', Journal of Discrete Mathematics and Its Applications, 10(3), pp. 243-261. doi: 10.22061/jdma.2025.11860.1123
CHICAGO
S. Arthur Abayo , I. Owino Okoth and D. Munyao Kasyoki, "Counting formulas for weakly labelled plane tree-like structures," Journal of Discrete Mathematics and Its Applications, 10 3 (2025): 243-261, doi: 10.22061/jdma.2025.11860.1123
VANCOUVER
Abayo, S. Arthur, Okoth, I. Owino, Kasyoki, D. Munyao Counting formulas for weakly labelled plane tree-like structures. Journal of Discrete Mathematics and Its Applications, 2025; 10(3): 243-261. doi: 10.22061/jdma.2025.11860.1123
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