Minimum Roman Dominating Distance Energy of a Graph

TL;DR

This paper introduces the concept of minimum roman dominating distance energy for graphs, analyzes its properties, computes it for standard graphs, and establishes bounds for this new graph invariant.

Contribution

It defines the minimum roman dominating distance energy of a graph, explores its properties, and provides bounds, which is a novel contribution to graph energy studies.

Findings

Computed minimum roman dominating distance energy for standard graphs.

Analyzed eigenvalue properties of the associated matrix.

Derived upper and lower bounds for the energy.

Abstract

In this correspondence, we introduced the concept of minimum roman dominating distance energy $E_{RDd}(G)$ of a graph $G$ and computed minimum roman dominating distance energy of some standard graphs. Also, we discussed the properties of eigenvalues of a minimum roman dominating distance matrix $A_{RDd}(G).$ Finally, we derived the Upper and lower bounds for $E_{RDd}(G).$