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 $K_{n}^{+-+}$.
📌 3 Key Takeaways
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Objective & Hypothesis: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.
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Key Findings & Data:The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of $G$ and is denoted by $\gamma_{it}(G)$.
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Conclusion & Impact: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 $K_{n}^{+-+}$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domination number · independent transversal domination number · independence number
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 $K_{n}^{+-+}$.
Atakul, B. A. (2022). Independent Transversal Domination Number for Some Transformation Graphs $G^{xyz}$ when xyz=+-+. Turkish Journal of Mathematics and Computer Science, Volume: 14 Issue: 1. https://doi.org/10.47000/tjmcs.796501
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