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Analyzing Energy and Defining New Classes of Borderenergetic Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 30 اردیبهشت 1405 اصل مقاله (474.58 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30915.2666 | ||
| نویسندگان | ||
| Yasir Bashir1؛ Bilal A. Chat* 1؛ Hilal A. Ganie2 | ||
| 1Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir, India | ||
| 2Department of Mathematics, Govt. Degree College Uri, JK Government, India | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| graphs؛ rank؛ eigenvalues؛ energy؛ topological index | ||
| مراجع | ||
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