The Laplacian Minimum Pendant Dominating Energy of a Graph

Abstract

Let  be any graph. The pendant dominating set and the associated Laplacian minimum pendant dominating energy (denoted as ) provide insights into both the structure of the graph and the energy associated with specific dominating sets. Here’s an overview of the key concepts and bounds related to . The study of  involves understanding the spectral properties of the Laplacian matrix relative to pendant dominating sets. By calculating exact values for standard graph families and establishing bounds, one gains deeper insights into both the structural and spectral characteristics of graphs.