Abstract: For a graph G and a positive integer k, a subset S of vertices of G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. The cardinality of a minimum k-path vertex cover is denoted by k(G). In this paper, we give some bounds and the exact values in special cases for k of the Cartesian, and lexicographic products of some graphs.
DOI: *As the DOI is a unique identifier, it is already available in the pdf version. **The DOI link will be activated in the first midst of January 2026.