Name: Swaroopa Rani N.C.
Country: India

Year: 2026
Volume: Volume-16, (March) Year-2026 (Special Issue: Business Collaboration in a VUCA World: Redefining Sustainable Organizational Growth)
Page Number: 424-428
DOI: https://doi.org/10.5281/zenodo.21849207

ABSTRACT
The eigenvalue of a graph G is the eigenvalue of its adjuency matrix. The energy E(G) of G is the sum of absolute values of the elgenvalues. A natural question arises: How the energy of a given graph G can be related with the graph obtained from G by means of some graph operations? In order to answer this question, we have considered two graphs namely, splitting graph S(G) and shadow graph D_2 (G). It has been proven that E(S'(G))=√5 E(G) and E(D_2 (G))=2E(G).

1. INTRODUCTION
All graphs considered here are simple, finite and undirected. For standard terminology and notations related to graph theory, we follow Balakrishnan and Ranganathan [2] while for algebra we follow Lang [7].

The Adjacency matrix A(G) of a graph G with vertices v_1,v_2…..v_n is an n × n matrix [a_ij] such that a_ij=1 if v_i is adjacent to v_j , and 0 otherwise.

The eigenvalues λ_1,λ_2……λ_n of the graph G are the eigenvalues of its adjacency matrix. The set of eigenvalues of the graph with thei