We show that every tree of order n ≥ 3 has at least ⌈ n / 2 ⌉ + 1 maximal dissociation sets and characterize the corresponding extremal graphs attaining this lower bound.
Mar 31, 2024
Apr 17, 2024 · A dissociation set of G is maximal if it is not a proper subset of any other dissociation sets. We show that every tree of order n ≥ 3 has at ...
A subset of vertices is called a maximum dissociation set if it induces a subgraph with vertex degree at most 1, and the subset has maximum cardinality. Zito ...
Nov 5, 2024 · This dissociation set is considered maximal if it is not contained within any other dissociation sets, or maximum if it has the largest possible ...
Nov 5, 2024 · A subset of vertices in a graph G is considered a maximal dissociation set if it induces a subgraph with vertex degree at most 1 and it is ...
Minimum number of maximal dissociation sets in trees ; Journal: Discrete Applied Mathematics, 2024, p. 272-278 ; Publisher: Elsevier BV ; Authors: Junxia Zhang, ...
Nov 8, 2024 · In this paper, it is shown that for n ≥ 3 n\geq 3 , every unicyclic graph contains a minimum of ⌊ n / 2 ⌋ + 2 \lfloor n/2\rfloor+2 maximal ...
Sep 30, 2020 · A subset of vertices is called a maximum dissociation set if it induces a subgraph with vertex degree at most 1, and the subset has maximum cardinality.
In this contribution we investigate the maximal number of maximum dissociation sets in forests with fixed order and dissociation number.
A subset of vertices is a maximum independent set if no two of the vertices are adjacent and the subset has maximum cardinality.