On the Square Free Detour Number of Windmill Graphs

The set \(S\) of vertices is said to be a square free detour set of \(G^*=( V^*,\,E^* )\) if \(I_{D_{f} } [S]=V^*\). The square free detour number of \(G^*\) is the cardinality of the minimum proper square free detour subset of \(V^*\). The square free detour number \(dnf (G^*)\), the connected square free detour number \(cdn_{f }(G^*)\) and the vertex square free detour number \(dn_{f_u }(G^*)\) of \(G^*\) are defined. Also, we determine the square free detour number, the connected square free detour number and the vertex-square free detour number of windmill graphs.