On the Domination Number of the Splitting Graph of C_ξ^κ

Abstract

This paper explores the domination number of the splitting graph associated with higher powers of cycle graphs. We begin by computing the domination number of the splitting graph of the square and cube of the cycle graph C_ξ. Through analysis and observed patterns, we propose a general conjecture regarding the domination number of the splitting graph of the κ^th power ofC_ξ. These results extend the existing work on domination parameters in transformed graphs and provide a foundation for further theoretical development and applications.