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A spectral excess theorem for digraphs with normal Laplacian matrices | ||
| Transactions on Combinatorics | ||
| مقاله 2، دوره 7، شماره 3، آذر 2018، صفحه 19-28 اصل مقاله (240.07 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2018.105873.1513 | ||
| نویسنده | ||
| Fateme Shafiei* | ||
| Isfahan University of Technology | ||
| چکیده | ||
| The spectral excess theorem, due to Fiol and Garriga in 1997, is an important result, because it gives a good characterization of distance-regularity in graphs. Up to now, some authors have given some variations of this theorem. Motivated by this, we give the corresponding result by using the Laplacian spectrum for digraphs. We also illustrate this Laplacian spectral excess theorem for digraphs with few Laplacian eigenvalues and we show that any strongly connected and regular digraph that has normal Laplacian matrix with three distinct eigenvalues, is distance-regular. Hence such a digraph is strongly regular with girth $g=2$ or $g=3$. | ||
| کلیدواژه‌ها | ||
| A Laplacian spectral excess theorem؛ Distance-regular digraphs؛ Strongly regular digraphs | ||
| مراجع | ||
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[21] G. R. Omidi, A spectral excess theorem for normal digraphs, J. Algebraic Combin., 42 (2015) 537–554. | ||
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