Analyzing Energy and Defining New Classes of Borderenergetic Graphs

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir, India

2 Department of Mathematics, Govt. Degree College Uri, JK Government, India

Abstract

In graph theory, the \textit{energy} of a graph \( G \), denoted as \( \mathcal{E}(G) \), is quantified by \(\mathcal{E}(G) = \sum_{i=1}^{n} |\lambda_i|\), where the eigenvalues \( \lambda_1, \lambda_2, \ldots, \lambda_n \) derive from the adjacency matrix of \( G \), and \( n \) represents the vertex total. This research investigates the conditions enabling line graphs of non-regular structures to transform into borderenergetic forms, emphasizing structural traits that drive this transition. The focus includes irregular graphs like the complete bipartite graphs \(K_{a,b}\) across varying \( a \) and \( b \). We also examine corona products, exemplified by \( K_{a,b} \circ K_r \), to identify conditions for the emergence of borderenergetic graphs, thus enhancing comprehension of these graphs through structural and spectral perspectives.

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References

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Communications in Combinatorics and Optimization

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Available Online from 20 May 2026

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