LAUSR

A vertex v of a graph $$G=(V,E)$$G=(V,E) is said to ve-dominate every edge incident to v, as well as every edge adjacent to these incident edges. A set $$S \subseteq V$$S⊆V is a vertex–edge dominating set (double vertex–edge dominating set, respectively) if every edge of E is ve-dominated by at least one vertex (at least two vertices) of S. The minimum cardinality of a vertex–edge dominating set (double vertex–edge dominating set, respectively) of G is the vertex–edge domination number $$\gamma _{ve}(G)$$γve(G) (the double vertex–edge domination number $$\gamma _{dve}(G)$$γdve(G), respectively). The influence of edge removal, edge addition and edge subdivision on the double vertex–edge domination number of a graph are investigated in this paper.