On the Dom-Chromatic number and its behavior in graphs derived from subdivision operations

Abstract

This paper studies the \textit{dom-chromatic number} of graphs formed through different subdivision operations. Exact values and simple bounds of $\gamma_{dc}(G)$ are found for basic graph families such as paths, cycles, complete graphs, and complete bipartite graphs. The effect of transformations like $k$-subdivision, iterated subdivision, middle, and central graphs on the dom-chromatic number is examined. The work also compares $\gamma_{dc}(G)$ with other known graph parameters such as the chromatic number, domination number, and distinguishing chromatic number. The results show how subdivision changes both domination and coloring properties, giving useful observations on color-based domination in transformed graphs.