Laplacian Minimum Independent Dominating Energy of Graphs

Abstract

If every vertex v\in V-S is adjacent to at least one vertex in S, then the set S subset of  V is a dominating set. An independent set of G is a set S subset V(G) in which no two of its vertices are adjacent. An independent dominating set is a dominating set that is also an independent set. A minimum independent dominating set is an independent dominating set with the least amount of cardinality. The Laplacian minimum independent dominating energy of a graph, denoted as LE_{D_{i}}(G), is introduced in this article, along with methods for calculating it for various types of graphs. Additionally, the upper and lower bounds of LE_{D_{i}}(G) are established.