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Graceful polynominals: an introduction and a glance at the graceful tree conjecture

Venerdì 11 gennaio 2019, ore 14.30, aula M1.6, edificio Matematica, Dipartimento FIM, Modena

Relatore: dott. Andrea Vietri ("Sapienza" Università di Roma)

Abstract: I will introduce a family of homogeneous polynomials for any given graph, with coefficients in Z2, one for every degree and with as many variables as the number of vertices. These “graceful" polynomials are related to graceful labellings: in some cases a graceful polynomial with all even coefficients (therefore vanishing (mod 2) ) could be an efficient tool for proving that the graph is non-graceful, in the same spirit as in a pioneering work by A. Rosa. More generally, graceful polynomials provide necessary conditions for gracefulness, so they might even play a role in finding some non-graceful tree... However, for the moment it seems interesting to classify vanishing polynomials having small degrees, and find some infinite classes of non-graceful graphs. I will also report on a strange behaviour of the lengths of these polynomials, for a fixed degree and over a random class of trees or general graphs.

Ospiti: Simona Bonvicini simona.bonvicini@unimore.it

[Ultimo aggiornamento: 01/04/2021 12:48:00]