Let  be a simple connected graph of order n with domination number  and let  A k-domination defect set of G is a nonempty set  of cardinality  such that  is minimum among the subsets of containing  vertices. The minimum number of vertices in G which are left undominated by S is denoted by  This paper presents results on the domination defect of graphs resulting from the composition product  of a connected graph G and any graph H. In particular, the k-domination defect set of is characterized and  is determined.

k-domination defect, minimum dominating set, composition of graphs.

Received: April 28, 2023; Revised: May 20, 2023: Accepted: June 8, 2023; Published: June 30, 2023

How to cite this article: Aldwin T. Miranda and Rolito G. Eballe, Domination defect in the composition of graphs, Advances and Applications in Discrete Mathematics 39(2) (2023), 209-219. http://dx.doi.org/10.17654/0974165823048

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