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AKCE International Journal of Graphs and Combinatorics Volume 20, 2023 - Issue 2: International Conference on Linear Algebra and its Applications; Guest editors: Ravindra B Bapat, Manjunatha Prasad Karantha,Stephen J Kirkland, Simo Puntanen, S Arumugam
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Research Articles

On singularity and properties of eigenvectors of complex Laplacian matrix of multidigraphs

Sasmita Barika School of Basic Sciences, IIT Bhubaneswar, Bhubaneswar, IndiaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-3927-5218View further author information
ORCID Icon,
Sane Umesh Reddya School of Basic Sciences, IIT Bhubaneswar, Bhubaneswar, IndiaView further author information
&
Gopinath Sahoob School of Computer Science Engineering and Technology, Bennett University, Greater Noida, IndiaView further author information
Pages 125-133 | Received 01 Jun 2023, Accepted 02 Jul 2023, Published online: 02 Aug 2023

References

  • Abreu, N. M. M. D. (2007). Old and new results on algebraic connectivity of graphs. Linear Algebra Appl. 423(1): 53–73.
  • Agaev, R., Chebotarev, P. (2010). Which digraphs with ring structure are essentially cyclic? Adv. Appl. Math. 45: 232–251.
  • Bapat, R. B., Kalita, D., Pati, S. (2012). On weighted directed graphs. Linear Algebra Appl. 436: 99–111.
  • Bapat, R. B., Pati, S. (1998). Algebraic connectivity and the characteristic set of a graph. Linear Multilinear Algebra. 45(2–3): 247–273.
  • Barik, S., Sahoo, G. (2020). A new matrix representation of multidigraphs. AKCE Int. J. Graphs Comb. 17(1): 466–479.
  • Bollobás, B. (1998). Modern Graph Theory. Graduate Texts in Mathematics, Vol. 184, 1st ed. New York: Springer.
  • Chebotarev, P. Y., Agaev, R. P. (2009). Coordination in multiagent systems and Laplacian spectra of digraphs. Autom. Remote. Control. 70(3): 136–151.
  • Cvetković, D. M., Doob, M., Sachs, H. (1980). Spectra of Graphs: Theory and Application. New York: Academic Press.
  • Dong, J. G., Lin, L. (2016). Laplacian matrices of general complex weighted directed graphs. Linear Algebra Appl. 510: 1–9.
  • Fiedler, M. (1973). Algebraic connectivity of graphs. Czechoslov. Math. J. 23(2): 298–305.
  • Fiedler, M. (1975). A property of eigenvectors of non-negative symmetric matrices and its application to graph theory. Czechoslov. Math. J. 25(4): 619–633.
  • Grone, R., Merris, R. (1987). Algebraic connectivity of trees. Czechoslov. Math. J. 37(4): 660–670.
  • Helmberg, C., Reiss, S. (2010). A note on Fiedler vectors interpreted as graph realizations. Oper. Res. Lett. 38(4): 320–321.
  • Horn, R. A., Johnson, C. R. (2013). Matrix Analysis. New York: Cambridge University Press.
  • Kalita, D. (2012). On 3-colored digraphs with exactly one nonsingular cycle. Electron. J. Linear Algebra. 23: 397–421.
  • Kalita, D. (2015). Properties of first eigenvectors and first eigenvalues of nonsingular weighted directed graphs. Electron. J. Linear Algebra. 30: 227–242.
  • Kalita, D., Pati, S. (2014). A reciprocal eigenvalue property for unicyclic weighted directed graphs with weights from {±1,±i}. Linear Algebra Appl. 449: 417–434.
  • Kirkland, S., Fallat, S. (1998). Perron components and algebraic connectivity for weighted graphs. Linear Multilinear Algebra. 44(2): 131–148.
  • Merris, R. (1987). Characteristic vertices of trees. Linear Multilinear Algebra. 22(2): 115–131.
  • Merris, R. (1994). Laplacian matrices of graphs: a survey. Linear Algebra Appl. 197: 143–176.
  • Mohar, B. (1992). Laplacian eigenvalues of graphs - a survey. Discrete Math. 109: 171–183.
  • Reff, N. (2012). Spectral properties of complex unit gain graphs. Linear Algebra Appl. 436(9): 3165–3176.
  • Sahoo, G. (2021). Complex adjacency spectra of digraphs. Linear Multilinear Algebra. 69(2): 193–207.
  • Su, L., Li, H.-H., Zheng, L.-R. (2012). The Laplacian spectrum of some digraphs obtained from the wheel. Discuss. Math. Graph Theory. 32: 255–261.

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