Upper Square Free Detour Number of Graphs

In this article we introduce the minimal square free detour sets and investigate the upper square free detour number of a graph. A square free detour set of vertices in a graph is called a minimal square free detour set if no proper subset is a square free detour set of the graph  The upper square free detour number is the maximum order of its minimal square free detour set of the graph. We also determine the upper square free detour number of standard graphs that supports robotics path planning and biological network analysis for efficient navigation.