Independent Transversal Domination Number for Some Transformation Graphs $G^{xyz}$ when xyz=+-+

Abstract

A dominating set of a graph $G$ which intersects every independent set of a maximum cardinality in $G$ is called an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of $G$ and is denoted by $\gamma_{it}(G)$. In this paper we investigate the independent transversal domination number for the transformation graph of the path graph $P_{n}^{+-+}$, the cycle graph $C_{n}^{+-+}$, the star graph $S_{1,n}^{+-+}$, the wheel graph $W_{1,n}^{+-+}$ and the complete graph $K_{n}^{+-+}$.