Power Dominator Chromatic Numbers of Splitting Graphs of Certain Classes of Graphs

Document Type : Short notes

Authors

1 Madras Christian College, Department of Mathematics, Tambaram, Chennai 600059 INDIA

2 Honorary Visiting Professor, Liverpool Hope University, Liverpool, L169JD, UK

3 Professor, School of Mathematics, Computer Science Engineering, Liverpool Hope University, Liverpool L16 9JD, UK

4 Honorary Visiting Professor, Liverpool Hope University, Liverpool , L169JD, UK

Abstract

Domination in graphs and coloring of graphs are two main areas of investigation in graph theory. Power domination is a variant of domination in graphs introduced in the study of the problem of monitoring an electric power system. Based on the notions of power domination and coloring of a graph, the concept of power dominator coloring of a graph was introduced. The minimum number of colors required for power dominator coloring of a graph $G$ is called the power dominator chromatic number $\chi_{pd}(G)$ of $G,$ which has been computed for some classes of graphs. Here we compute the power dominator chromatic number for splitting graphs of certain classes of graphs.

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References

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Communications in Combinatorics and Optimization
Volume 9, Issue 2
June 2024
Pages 317-327

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