2014/12/28 by Saieed Akbari, Pooyan Ehsani, Akbari, Saieed +7
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.1412.8203
openalex publication_date 2014/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a graph. A subset S ⊆ V(G) is called a total dominating set if every vertex of G is adjacent to at least one vertex of S. The total domination number, γt(G), is the minimum cardinality of a total dominating set of G. In this paper using a greedy algorithm we provide an upper bound for γt(G), whenever G is a bipartite graph and δ(G) ≥ k. More precisely, we show that if k > 1 is a natural number, then for every bipartite graph G of order n and δ(G) ≥ k, γt(G) ≤ n(1- \frack!∏i=0k-1((k)/(k-1)+i)).