2014/10/05 by Saeid Alikhani, Alikhani, Saeid, Davood Fatehi +1
Computer Science · Mathematics · #05C60 #05C69 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1410.1169
openalex publication_date 2014/10/05 · openalex created_date 2016/09/23 · openalex updated_date 2026/07/28
Let G=(V,E) be a graph. A set S⊆ V(G) is a dominating set, if every vertex in V(G)\backslash S is adjacent to at least one vertex in S. The k-dominating graph of G, Dk (G), is defined to be the graph whose vertices correspond to the dominating sets of G that have cardinality at most k. Two vertices in Dk(G) are adjacent if and only if the corresponding dominating sets of G differ by either adding or deleting a single vertex. In this paper we consider and study the n-dominating graph of specific graphs.