Laplacian Minimum Split Dominating Energy of Graphs

Abstract

For a graph G, a subset D of V(G) is called a split dominating set if the induced graph <V-D> is disconnected. The split domination number  is the minimum cardinality of a split domination set. In this paper we introduce the Laplacian minimum split dominating energy LE_s (G) of a graph G and computed Laplacian minimum split dominating energies of some standard graphs. Upper and lower bounds for LE_s (G) are established.