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Total dominating functions of graphs: antiregularity versus regularity
2020
Contributions to Mathematics
A set S of vertices in a nontrivial connected graph G is a total dominating set if every vertex of G is adjacent to some vertex of S. The minimum cardinality of a total dominating set for G is the total domination number of G. A function for every two vertices u and v of G. While no graph possesses an irregular total dominating function, a graph G has an antiregular total dominating function h if there are exactly two vertices u and v of G such that σ h (u) = σ h (v). It is shown that for every
doi:10.47443/cm.2020.0045
fatcat:fg6akhuhj5e3zfqokrl42mbrtq