ON ZAGREB ENERGIES OF SOME GRAPH OPERATIONS

Document Type : Original Manuscript

Authors

Department of Mathematics, Dibrugarh University, Assam, India.

10.22044/jas.2024.14103.1799

Abstract

Recently, Zagreb energies, a graph invariant based on the eigenvalues of the Zagreb matrices have been proposed as an analogous to graph energy. In this communication, the Zagreb energies and Zagreb spectral radius are examined in relation to a number of graph operations, such as m-splitting graphs, m-shadow graphs, m-duplicate graphs, and extended bipartite double graphs. Further, we explore these generalised graphs within the context of specific graph types such as complete graphs, complete bipartite graphs, cycle graphs, and the complements of cycle graphs. Furthermore, we report an error present in [19] that contradicts the claim of hyperenergetic behaviour for the splitting graph of regular graphs, and also establish the non-hyperenergetic behaviour of the m-shadow graph.

Keywords

References

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Journal of Algebraic Systems
Volume 14, Issue 3
June 2026
Pages 383-406

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