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

Year 2022, , 1 - 7, 30.06.2022

Betül Atay Atakul

https://doi.org/10.47000/tjmcs.796501

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 $K_{n}^{+-+}$.

Keywords

Domination number, independent transversal domination number, independence number

References

• Ahangar, H. A., Samodivkin, V., Yero, I. G., Independent transversal dominating sets in graphs: Complexity and structural properties, Filomat, 30(2)(2016), 293-303.
• Aytaç, A., Atakul Atay, B., Exponential domination critical and stability in some graphs, International Journal of Foundations of Computer Science, 30(2019), 731-791.
• Aytaç, A., Turacı, T., Bondage and strong-weak bondage numbers of transformation graphs G^{xyz}, International Journal of Pure and Applied Mathematics, 106(2)(2016), 689-698.
• Aytaç, A., Turacı, T., Vulnerability measures of transformation graph G^{xy+}$, International Journal of Foundations of Computer Science, 26(2)(2015), 667-675.
• Baoyindureng, W., Zhang, L., Zhang, Z., The Transformation graph G^{xyz}$when xyz=-++, Discrete Mathematics, 296(2005), 263-270.
• Brause, C., Henning, M., Ozeki, K., Schiermeyer, I., E. Vumar, On upper bounds for the independent transversal domination number}, Discrete Applied Mathematics, 236(2018), 66-72.
• Chartrand, G., Lesniak, L., Graphs and Digraphs, Fourth Edition, 2005.
• Chartrand, G., Zhang, P., Introduction to Graph Theory, McGraw-Hill, Boston, Mass, USA, 2005.
• Dankelmann, P., Day, D., Erwin, D., Mukwembi, S., Swart, H., Domination with exponential decay}, Discrete Mathematics, 309(2009), 5877-5883.
• Hamid, I. S, Independent transversal domination in graphs, Discussiones Mathematicae Graph Theory, 32(2012), 5-7.
• Harary F., Graph Theory, Addition-Wesley Publishing Co., Reading, MA/Menlo Park, CA/London, 1969.
• Haynes, T. W., Hedeniemi, S. T., Slater, P. J., Fundamentals of Domination in Graphs, Marcel Dekker, Inc, New York, 1998.
• Henning, M. A, Domination in Graphs: a survey. Cong. Number, In G. Chartrand and M. Jacobson, editors, Surveys in Graph Theory, 116 (1996), 139-172.
• Jebitha, M. K. A., Joseph, J. P., Domination in transformation graph G^{+-+}$, International J. Math. Combin., 1(2012), 58-73.
• Lan, X., Baoyindureng, W., Transformation graph G^{-+-}, Discrete Mathematics, 308(2008), 5144-5148.
• West, D. B., Introduction to Graph Theory (Second Edition), 2001.