Abstract
A subset of vertices in a graph G is called a maximum dissociation set if it induces a subgraph with vertex degree at most 1 and the subset has maximum cardinality. The dissociation number of G, denoted by \(\psi (G)\), is the cardinality of a maximum dissociation set. A subcubic tree is a tree of maximum degree at most 3. In this paper, we give the lower and upper bounds on the dissociation number in a subcubic tree of order n and show that the number of maximum dissociation sets of a subcubic tree of order n and dissociation number \(\psi \) is at most \(1.466^{4n-5\psi +2}\).
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Funding
This work was supported by Beijing Natural Science Foundation (No. 1232005), Research Foundation for Advanced Talents of Beijing Technology and Business University (No. 19008023211), National Key Research and Development Program of China (2019YFC1906102), and National Key Technology Research and Development Program of the Ministry of Science and Technology of China (No. 2015BAK39B00).
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Zhang, L., Tu, J. & Xin, C. Maximum dissociation sets in subcubic trees. J Comb Optim 46, 8 (2023). https://doi.org/10.1007/s10878-023-01076-9
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DOI: https://doi.org/10.1007/s10878-023-01076-9