Domination Scattering Number in Graphs

Scattering number measures the stability of a graph by determining how well vertices are spread throughout the graph. However, it may not always be distinctive for different graphs, especially when comparing the same scattering numbers. In this study, we aim to provide a more nuanced and sensitive measure of stability for graphs by introducing domination scattering numbers, a new measure of graph stability. This parameter likely captures additional structural characteristics or dynamics within the graph that contribute to its stability or resilience. Moreover, we investigate the domination scattering numbers of the graphs $P_n$, $C_n$, $K_{1,n}$, $K_{m,n}$, and $P_n\times C_3$.