Transversal Semitotal Domination Number in Graphs

Year 2025, Issue: 52, 1 - 8, 30.09.2025

Zeliha Kartal Yıldız

https://doi.org/10.53570/jnt.1720611

Abstract

A transversal semitotal dominating set in a graph $G$ is a subset of vertices that intersects every minimal semitotal dominating set of \( G \) and itself forms a semitotal dominating set. Among all sets that intersect each semitotal dominating set of a graph \( G \), the one with the smallest cardinality defines a key parameter in the present study. This parameter is referred to as the transversal semitotal domination number and is denoted by \( \gamma_{tt2}(G) \). This paper investigates fundamental properties of this parameter in arbitrary graphs and determines exact values of \( \gamma_{tt2}(G) \) for several standard graph classes, including complete, star, wheel, cycle, path, and complete bipartite graphs.

Keywords

Graph theory , domination , semitotal domination , transversal semitotal domination

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