PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2015 | 35 | 1 | 43-53
Tytuł artykułu

α-Labelings of a Class of Generalized Petersen Graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An α-labeling of a bipartite graph Γ of size e is an injective function f : V (Γ) → {0, 1, 2, . . . , e} such that {|ƒ(x) − ƒ(y)| : [x, y] ∈ E(Γ)} = {1, 2, . . . , e} and with the property that its maximum value on one of the two bipartite sets does not reach its minimum on the other one. We prove that the generalized Petersen graph PSn,3 admits an α-labeling for any integer n ≥ 1 confirming that the conjecture posed by Vietri in [10] is true. In such a way we obtain an infinite class of decompositions of complete graphs into copies of PSn,3.
Wydawca
Rocznik
Tom
35
Numer
1
Strony
43-53
Opis fizyczny
Daty
wydano
2015-02-01
otrzymano
2013-02-21
poprawiono
2014-01-13
zaakceptowano
2014-01-29
online
2015-02-06
Twórcy
autor
  • DICATAM - Sezione di Matematica Università degli Studi di Brescia Via Valotti 9, I-25133 Brescia, Italy, anna.benini@unibs.it
  • DICATAM - Sezione di Matematica Università degli Studi di Brescia Via Valotti 9, I-25133 Brescia, Italy, anita.pasotti@unibs.it
Bibliografia
  • [1] P. Adams and D.E. Bryant, The spectrum problem for the Petersen graph, J. Graph Theory 22 (1996) 175-180. doi:10.1002/(SICI)1097-0118(199606)22:2h175::AID-JGT8i3.0.CO;2-K[Crossref]
  • [2] A. Bonisoli, M. Buratti and G. Rinaldi, Sharply transitive decompositions of complete graphs into generalized Petersen graphs, Innov. Incidence Geom. 6/7 (2007/08) 95-109.
  • [3] D. Bryant and S. El-Zanati, Graph decompositions, in: CRC Handbook of Combi- natorial Designs (C.J. Colbourn and J.H. Dinitz Eds.), CRC Press, Boca Raton, FL (2006) 477-486.
  • [4] R. Frucht and J.A. Gallian, Labeling prisms, Ars Combin. 26 (1988) 69-82.
  • [5] J.A. Gallian, A dynamic survey of graph labelings, Electron. J. Combin. 16 (2013) DS6.
  • [6] T.A. Redl, Graceful graphs and graceful labelings: Two mathematical programming formulations and some other new results, Congr. Numer. 164 (2003) 17-31.
  • [7] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967) 349-355.
  • [8] A. Vietri, A new infinite family of graceful generalised Petersen graphs, via “graceful collages” again, Australas. J. Combin. 41 (2008) 273-282.
  • [9] A. Vietri, Erratum: A little emendation to the graceful labelling of the generalised Petersen graph P8t,3 when t = 5: “Graceful labellings for an infinite class of general- ized Petersen graphs” [Ars. Combin. 81 (2006), 247-255; MR2267816], Ars Combin. 83 (2007) 381.
  • [10] A. Vietri, Graceful labellings for an infinite class of generalised Petersen graphs, Ars Combin. 81 (2006) 247-255.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1776
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.