Edge domination number and the number of minimum edge dominating sets in pseudofractal scale-free web and Sierpinski Gasket

As a fundamental research object, the minimum edge dominating set (MEDS) problem is of both theoretical and practical interest. However, determining size MEDS number all MEDSs in general graph NP-hard, it thus makes sense to find special graphs for which can be exactly solved. In this paper, we study analytically pseudofractal scale-free web Sierpiński gasket with same vertices edges. For graphs, obtain exact expressions domination number, as well recursive solutions distinct MEDSs. web, one-ninth edges, three-fifths gasket. Moreover, also less than that corresponding We argue difference between two studied lies topology.