05C50 Online Seminar: Leonardo de Lima

  • Date: 03/08/2024
  • Time: 08:00
Leonardo de Lima, Federal University of Paraná (Brazil)



On graphs with an eigenvector whose entries are only {-1,0,1}


In 1986, Wilf posed the following question ``Which graphs have eigenvectors with entries solely -1 and +1?''. Stevanovic (2016) showed that the problem of finding such graphs is NP-Hard. Caputo, Khames, and Knippel (2019) described all graphs whose Laplacian matrix has an eigenvector with entries only -1 and +1 and apparently, they did not know Wilf's question related to the adjacency matrix. In this talk, we answer Wilf's question for the adjacency and the signless Laplacian matrix. Also, we give a characterization of all graphs having an eigenvector with entries only in {-1,0,1}. Our results point out an interesting relation of the graphs with these kinds of eigenvectors to the degree sequence of the graph.

Other Information: 

The 05C50 Online is an international seminar about graphs and matrices held twice a month on Fridays.


Time: 8AM Pacific/10AM Central 


For more information, visit https://sites.google.com/view/05c50online/home


If you would like to attend, please register using this form to receive the zoom links: https://docs.google.com/forms/d/e/1FAIpQLSdQ98fh58cgeSWzbFe3t77i28FXDck1gYuX9jv_qd4kEf5l_Q/viewform?usp=sf_link