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Published online by Cambridge University Press: 13 September 2024
In an isolate-free graph G, a subset S of vertices is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number of G, denoted by $\gamma _{t2}(G)$, is the minimum cardinality of a semitotal dominating set in G. Goddard, Henning and McPillan [‘Semitotal domination in graphs’, Utilitas Math. 94 (2014), 67–81] characterised the trees and graphs of minimum degree 2 with semitotal domination number half their order. In this paper, we characterise all graphs whose semitotal domination number is half their order.
This work was funded in part by National Natural Science Foundation of China (Grant No. 12071194) and the Chongqing Natural Science Foundation Innovation and Development Joint Fund (Municipal Education Commission) (Grant No. CSTB2022NSCQ-LZX0003).