O uso de ferramentas computacionais na construção de contraexemplos para um teorema de Fiedler-Nikiforov sobre grafos hamiltonianos

In this article, counterexamples are presented for the reciprocal of a Fiedler-Nikiforov result that deals with an inequality involving the concepts of spectral radius of graphs and its hamiltonicity. For this, two different methods were used to obtain the results. The first was made based on results given by Scilab that determined the non-validity of the Fiedler-Nikiforov inequality. In the second, basic concepts and results of mathematical analysis were used. In addition, the concepts of maximum click of a graph and its relation to the spectral radius were used to construct counterexamples. This work was carried out in the period between the years 2017 and 2019 and was part of a PICME project in which the second author developed her research and monograph in the area of Graph Theory.