Year: 2026
Type: article
Abstract: The accurate isolate domination number combines isolate domination with a complement-based accuracy condition. We establish a cardinality criterion for existence and characterize graphs with parameter one through unique universal vertices, yielding a corresponding result for graph joins. Our principal result gives a complete classification for complete multipartite graphs: the parameter exists exactly when at least one partite size occurs uniquely, and its value is the least uniquely occurring size. Consequently, \gamma_{a0}(K_{r,s})=\min\{r,s\} for r\neq s, whereas the parameter does not exist for balanced complete bipartite graphs.
Authors: Jamil Hamja, Arman Tarang, Sisteta Kamdon
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W7202283071