Existence of independent [1, 2]-sets in caterpillars

• Main Authors: Santoso, Eko Budi, Marcelo, Reginaldo M
• Format: text
• Published: Archīum Ateneo 2016
• Subjects: Number Theory
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/79; https://aip.scitation.org/doi/abs/10.1063/1.4940820
• Institution: Ateneo De Manila University

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 in...