On the Square Free Detour Number of Windmill Graphs - Rani, K. Christy; Pacifica, G. Priscilla (Communications in Mathematics and Applications, 2023)
The set \(S\) of vertices is said to be a square free detour set of \(G^*=( V^*,\,E^* )\) if \(I_{D_{_{ \square f}} } [S]=V^*\). 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 \(dn_{\square f} (G^*)\), the connected square free detour number \(cdn_{_{\square f} }(G^*)\) and the vertex square free detour number \(dn_{_{\square f_u} }(G^*)\) 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.
Keywords: Square free detour number; Connected square free detour number; Vertex square free detour number