2018/04/07 by Doost Ali Mojdeh, Mojdeh, Doost Ali, Seyed Reza Musawi +5
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1804.02532
openalex publication_date 2018/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A subset D of vertices of a graph G is a dominating set if for each u∈ V(G)∖ D, u is adjacent to some vertex v∈ D. The dominating number, γ(G) of G, is the minimum cardinality of a dominating set of G. A set D⊆ V(G) is a total dominating set if for each u∈ V(G), u is adjacent to some vertex v∈ D. the The total dominating number, γt(G) of G, is the minimum cardinality of a total dominating set of G. For an even integer n≥2 and 1≤Δ≤\lfloorlog2n\rfloor, a Knödel graph WΔ,n is a Δ-regular bipartite graph of even order n, with vertices (i,j), for i=1,2 and 0≤ j≤ n/2-1, where for every j,0≤ j≤ n/2-1,there is an edge between vertex (1,j) and every vertex (2,j+2k-1 (mod(n/2)), for k=0,1,⋯,Δ-1. In this paper, we determine the total domination number in 3-regular Knödel graphs W3,n.