(R2139) Italian Domination Number for Some Classes of Trees

Authors

• Amritha Prakash, Vellore Institute of Technology, India
• Ragukumar Pandurangan, Vellore Institute of Technology, India

Abstract

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 for bipartite graphs, it is NP-Complete to find the exact value of the Italian domination number. In this paper we identify the Italian domination number of some classes of trees.

Recommended Citation

Prakash, Amritha and Pandurangan, Ragukumar (2025). (R2139) Italian Domination Number for Some Classes of Trees, Applications and Applied Mathematics: An International Journal (AAM), Vol. 21, Iss. 1, Article 17.
Available at: https://digitalcommons.pvamu.edu/aam/vol21/iss1/17