Laplacian Minimum Dominating Quotient Energy of a Graph

Abstract

In this paper, we present the idea of Laplacian minimum dominating quotient energy of graph,  and compute the Laplacian minimum dominating quotient energy of  of few families of graphs. Additionally, we derive bounds for the Laplacian minimum dominating quotient energy, providing a comprehensive understanding of its behavior and properties in different graph structures.

Objectives: Finding the Laplacian minimum dominating quotient energy of different graph

Methods: To establish the upper and lower bounds for the energy of graphs we employ the Standard methods of proofs namely direct methods and using Matlab to compute the minimum pendant dominating partition eigen values of a graph .

Results: We obtain the Laplacian minimum dominating quotient energy of  of well-known families of graphs.  Additionally we obtain upper and lower bounds

Conclusions: Nowadays, the study of theory of domination and energy of graph is an important area in Graph theory and also remarkable research is going on in this area. In recent years many scholars are working in this area and also they are introducing new domination parameters.  In this paper we have initiated the study of Laplacian minimum dominating quotient energy of graph. We have calculated the energies for some standard family graphs and we have established some bounds for this parameter. Further, we have studied some important properties of Laplacian minimum quotient dominating eigenvalues