Exploring Prism Graphs with Fractional Domination Parameters

In this paper, we consider the prism graph of the cartesian product <img src=image/13437788_01.gif> as <img src=image/13437788_02.gif>. Our primary objectives are to explore the concept of the fractional domination number in the prism graphs by determining the bounds and relations of fractional domination number and other parameters in prism graphs. This makes significant improvements in resource allocation. To attain our objectives, we compute the bounds based on the definitions of the fractional domination number and other parameters. When comparing these parameters in prism graphs, we investigate how the fractional domination number relates to other parameters, such as the fractional mixed domination number, domination number, independence domination number, and vertex independence number of prism graphs. Our main findings include the domination chain of the prism graph, and also insights into how the bounds of the fractional domination number and the fractional mixed domination number change when the vertex or edge is added or removed from the prism graphs which is crucial for analyzing how changes in prism graphs affect the bounds of fractional domination-related parameters.