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On the coefficients of skew Laplacian characteristic polynomial of digraphs.
- Source :
- Discrete Mathematics, Algorithms & Applications; Jul2023, Vol. 15 Issue 5, p1-14, 14p
- Publication Year :
- 2023
-
Abstract
- Let G be a connected graph with n vertices and m edges. Let G ⃗ be the digraph obtained by orienting the edges of G arbitrarily. The digraph G ⃗ is called an orientation of G or oriented graph corresponding to G. The skew Laplacian matrix of the digraph G ⃗ is denoted by S L ̃ (G ⃗) and is defined as S L ̃ (G ⃗) = D ̃ (G ⃗) − S (G ⃗) , where S (G ⃗) is the skew matrix and D ̃ (G ⃗) is the diagonal matrix with i th diagonal entry d i + − d i − . In this paper, we obtain combinatorial representation for the first five coefficients of characteristic polynomial of skew Laplacian matrix of G ⃗. We provide examples of orientations of some well-known graphs to highlight the importance of our results. We conclude the paper with some observations about the skew Laplacian spectral determinations of the directed path and directed cycle. [ABSTRACT FROM AUTHOR]
- Subjects :
- POLYNOMIALS
GRAPH connectivity
LAPLACIAN matrices
DIRECTED graphs
Subjects
Details
- Language :
- English
- ISSN :
- 17938309
- Volume :
- 15
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Discrete Mathematics, Algorithms & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 163853403
- Full Text :
- https://doi.org/10.1142/S1793830922501312