Independent Domination Subdivision in Graphs

Abstract A set S of vertices in a graph G is dominating if every vertex not ad jacent to . If, addition, an independent set, then set. The domination number i ( ) the minimum cardinality subdivision $$ \hbox {sd}_{\mathrm{i}}(G)$$ sd i ( G ) edges that must be subdivided (each edge can at most once) order increase number. We show for connected on least three vertices, parameter well defined and differs significantly from well-studied $$\mathrm{sd_\gamma }(G)$$ sd γ For example, block graph, }(G) \le 3$$ ≤ 3 , while arbitrary large. Further we there exist with arbitrarily large maximum degree $$\Delta (G)$$ Δ such {sd}_{\mathrm{i}}(G) \ge 3 \Delta (G) - 2$$ ≥ - 2 contrast known result 2 1$$ 1 always holds. Among other results, present simple characterization trees T {sd}_{\mathrm{i}}(T) = T =