Maximum dissociation sets in subcubic trees

Lei Zhang (), Jianhua Tu () and Chunlin Xin ()
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Lei Zhang: Beijing Institute of Technology
Jianhua Tu: Beijing Technology and Business University
Chunlin Xin: Beijing University of Chemical Technology

Journal of Combinatorial Optimization, 2023, vol. 46, issue 1, No 8, 13 pages

Abstract: 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 $$\psi (G)$$ ψ ( 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 $$\psi $$ ψ is at most $$1.466^{4n-5\psi +2}$$ 1 . 466 4 n - 5 ψ + 2 .

Keywords: Extremal graph theory; Enumeration in graph theory; Maximum dissociation set; Trees (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-023-01076-9

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