Spanning Cactus Existence Problem on Flower Snark Graphs

A spanning cactus is a spanning substructure of a graph similar to a spanning tree of a graph. But it is more advantageous than the spanning tree in terms of reliability in network applications due to its higher edge connectivity. In genome expression analysis cactus graphs are widely used for important feature extraction and gene alignment. However, a graph may or may not contain a spanning cactus. Checking whether there exists a spanning cactus in a graph (SCEP) is an NP-Complete problem. In immediate past few years, the SCEP have been studied in various special graphs, such as Petersen graph, generalized Petersen graphs, \(3\times 3\times 3\) grid graph, Desargues graph, Windmill graphs etc. In this article, we have presented that there does not exist any spanning cactus when the considered graph is a Flower Snark Graph.