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

Document Type : Short notes

Authors

1 Department of Mathematics, Madras Christian College, Chennai 600 059, India

2 School of Mathematics, Computer Science and Engineering, Liverpool Hope University, Liverpool, L16 9JD, 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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