ON TRANSINVERSE OF MATRICES AND ITS APPLICATIONS | ||
| Journal of Algebraic Systems | ||
| دوره 12، شماره 1، آذر 2024، صفحه 135-147 اصل مقاله (150.94 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.12107.1629 | ||
| نویسندگان | ||
| Koombail Shahul Hameed* ؛ Kunhumbidukka Othayoth Ramakrishnan | ||
| Department of Mathematics, K M M Government Women’s College, Kannur, P.O. Box 670004, Kerala, India | ||
| چکیده | ||
| Given a matrix A with elements from a field of characteristic zero, the transin- verse A# of A is defined as the transpose of the matrix obtained by replacing the non-zero elements of A by their inverses and leaving zeros, if any, unchanged. We discuss the properties of this matrix operation in some detail and as an important application, we reinvent the celebrated matrix tree theorem for gain graphs. Characterization of balance in connected gain graphs using its Laplacian matrix becomes an immediate consequence. | ||
| کلیدواژهها | ||
| Gain graph؛ Signed graph؛ Graph eigenvalues؛ Graph Laplacian | ||
| مراجع | ||
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4. Yi Wang, Shi-Cai Gong and Yi-Zheng Fan, On the determinant of the Laplacian matrix of a complex unit gain graph, Discrete Math., 341 (2018), 81–86.
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6. T. Zaslavsky, Signed graphs, Discrete Appl. Math., 4(1) (1982), 47–74 | ||
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