Edge domination in some path and cycle related graphs (Q470539)

Summary: For a graph \(G=(V,E)\), a subset \(F\) of \(E\) is called an edge dominating set of \(G\) if every edge not in \(F\) is adjacent to some edge in \(F\). The edge domination number \(\gamma'(G)\) of \(G\) is the minimum cardinality taken over all edge dominating sets of \(G\). Here, we determine the edge domination number for shadow graphs, middle graphs, and total graphs of paths and cycles.