ENCLAVELESS SETS IN GRAPHS
Abstract
This study explores enclaveless sets in graphs, where a set is enclaveless if no vertex in S is an enclave, meaning no vertex has its closed neighborhood entirely contained within the set. The paper establishes general bounds for key parameters such as the enclaveless number, independence number, and domination number, and provides characterizations for various families of graphs, including paths, cycles, complete graph, bipartite graph, and star graph. Exact formulas are derived, including Nordhaus-Gaddum-type inequalities for the enclaveless number. The study also examines the relationship between enclaveless sets and graph connectivity.
Fields of Study & Subjects
Advanced Graph Theory Research
Graph Labeling and Dimension Problems
Graph theory and applications
Publication details
- Journal / source
- Far East Journal of Mathematical Sciences (FJMS)
- Volume
- 143
- Issue
- 4
- Pages
- 1039–1055
- Publication date
- 11 March 2026
- Language
- EN