Every graph can be associated with a family of homogeneous polynomials, one for every degree, having as many variables as the number of vertices. These polynomials are related to graceful labellings: a graceful polynomial with all even coefficients is a basic tool, in some cases, for proving that a graph is non-graceful, and for generating a possibly infinite class of non-graceful graphs. Graceful polynomials also seem interesting in their own right. In this paper we classify graphs whose graceful polynomial has all even coefficients, for small degrees up to 4. We also obtain some new examples of non-graceful graphs.

On the graceful polynomials of a graph / Vietri, Andrea. - In: TEH AUSTRALASIAN JOURNAL OF COMBINATORICS. - ISSN 1034-4942. - 73:2(2019), pp. 261-273.

On the graceful polynomials of a graph

Andrea Vietri
2019

Abstract

Every graph can be associated with a family of homogeneous polynomials, one for every degree, having as many variables as the number of vertices. These polynomials are related to graceful labellings: a graceful polynomial with all even coefficients is a basic tool, in some cases, for proving that a graph is non-graceful, and for generating a possibly infinite class of non-graceful graphs. Graceful polynomials also seem interesting in their own right. In this paper we classify graphs whose graceful polynomial has all even coefficients, for small degrees up to 4. We also obtain some new examples of non-graceful graphs.
2019
Graph, Graceful labelling, Graceful graph
01 Pubblicazione su rivista::01a Articolo in rivista
On the graceful polynomials of a graph / Vietri, Andrea. - In: TEH AUSTRALASIAN JOURNAL OF COMBINATORICS. - ISSN 1034-4942. - 73:2(2019), pp. 261-273.
File allegati a questo prodotto
File Dimensione Formato  
ajc_v73_p261-273.pdf

accesso aperto

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Altra licenza (allegare)
Dimensione 135.47 kB
Formato Adobe PDF
135.47 kB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1218324
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 0
social impact