Existence of independent [1, 2]-sets in caterpillars
Given a graph G, a subset S ⊆ V (G) is an independent [1, 2]-set if no two vertices in S are adjacent and for every vertex ν ∈ V (G)\S, 1 ≤ |N(ν) ∩ S| ≤ 2, that is, every vertex ν ∈ V (G)\S is adjacent to at least one but not more than two vertices in S. In this paper, we discuss the existence of independent [1, 2]-sets in a family of trees called caterpillars.
Santoso, E. B., & Marcelo, R. M. (2016, February). Existence of independent [1, 2]-sets in caterpillars. In AIP Conference Proceedings (Vol. 1707, No. 1, p. 020019). AIP Publishing LLC.