Set Theory Commons^™

(R2139) Italian Domination Number For Some Classes Of Trees, Amritha Prakash, Ragukumar Pandurangan

Applications and Applied Mathematics: An International Journal (AAM)

For a graph G with vertex set V , an Italian dominating function is a function f from V to {0, 1, 2} which has the property that for every vertex which is assigned 0, it must either adjacent to a vertex assigned 2 under f or adjacent to at least two vertices assigned 1 under f. The weight of an Italian dominating function is the sum of all weights assigned to the vertices. The minimum weight of an Italian dominating function f is the Italian domination number. Finding a graph’s Italian domination number is a well-known NP-Complete problem. Even …