On Characteristic Polynomial of Antiadjacency Matrix of A Line Digraph

Muhammad Irfan Arsyad Prayitno, Kiki Ariyanti Sugeng

Abstract


In this paper, we find the characteristic polynomial of the antiadjacency matrix of a line digraph. There are recent studies on the relation between the characteristic polynomial of the adjacency matrix and its line digraph, we are also interested in finding the connection between the antiadjacency matrix of a digraph and its line digraph. In this paper, we show the connection of characteristic polynomial of the antiadjacency matrix between an acyclic digraph and its line digraph.

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References


R. B. Bapat, Graphs and matrices, Vol. 27, Springer, 2010.

S. Budiyanto, S. Utama, S. Aminah, Eigenvalues of antiadjacency matrix of directed cyclic dumbbell graph, in: Journal of Physics: Conference Series, Vol. 1108, IOP Publishing, 2018, p. 012015.

Murni, A. E. Hadi, I. Febry, Abdussakir, Anti-adjacency and laplacian spectra of inverse graph of group of integers modulo n, in: IOP Conference Series: Materials Science and Engineering, Vol. 807, IOP Publishing, 2020, p. 012033.

B. H. Aji, K. A. Sugeng, S. Aminah, Characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic flower vase graph, in: Journal of Physics: Conference Series, Vol. 1722, IOP Publishing, 2021, p. 012055.

A. Deng, M. Feng, A. Kelmans, Adjacency polynomials of digraph transformations, Discrete Applied Mathematics 206 (2016) 15–38.

D. Bravo, F. Cubr ́ıa, M. Fiori, V. Trevisan, Complementarity spectrum of digraphs, Linear Algebra and its Applications 627 (2021) 24–40.

C. Dalf ́o, M. A. Fiol, M. Miller, J. Ryan, J. ˇSir ́aˇn, An algebraic approach to lifts of digraphs, Discrete Applied Mathematics 269 (2019) 68–76.

J. Bang-Jensen, G. Z. Gutin, Digraphs: theory, algorithms and applications, Springer Science & Business Media, 2008.

D. Ferrero, Introduction to interconnection network models, Publ. Mat. Urug 99 (1999) 25.

C. Balbuena, D. Ferrero, X. Marcote, I. Pelayo, Algebraic properties of a digraph and its line digraph, Journal of Interconnection Networks 4 (04) (2003) 377–393.

F. Zhang, G. Lin, When a digraph and its line digraph are connected and cospectral, Discrete Mathematics 184 (1-3) (1998) 289–295.

S. Severini, On the structure of the adjacency matrix of the line digraph of a regular digraph, Discrete Applied Mathematics 154 (12) (2006) 1763–1765.

R. A. Horn, C. R. Johnson, Matrix analysis, Cambridge university press, 2013.

J. A. Bondy, U. S. R. Murty, Graph theory, volume 244 of, Graduate Texts in Mathematics 623 (2008).

G. Chartrand, L. Lesniak, P. Zhang, Graphs & digraphs, vol. 39 (2010).

G. Chartrand, P. Zhang, A first course in graph theory, Courier Corporation, 2013.

G. Chartrand, P. Zhang, Chromatic graph theory, Second Edition, Chapman and Hall/CRC, 2019.

M. A. Fiol, L. A. Yebra, A. De Miquel, Line digraph iterations and the (d, k) digraph problem, IEEE Transactions on Computers 100 (5) (1984) 400–403




DOI: https://doi.org/10.25077/jmu.11.1.74-81.2022

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