2017/05/02 by Douglas J. Klein, Klein, Douglas J., Juan A. Rodríguez‐Velázquez +3 · 1 citation
Computer Science · #05C69 #05C70 #05C76 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.1705.00928
openalex publication_date 2017/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The open neighbourhood of a vertex v of a graph G is the set N(v) consisting of all vertices adjacent to v in G. For D⊆ V(G), we define D=V(G)∖ D. A set D⊆ V(G) is called a super dominating set of G if for every vertex u∈ D, there exists v∈ D such that N(v)∩ D=\u\. The super domination number of G is the minimum cardinality among all super dominating sets in G. In this article, we obtain closed formulas and tight bounds for the super domination number of G in terms of several invariants of G. Furthermore, the particular cases of corona product graphs and Cartesian product graphs are considered.