PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

Discussiones Mathematicae Graph Theory

2006 | 26 | 3 | 449-456
Tytuł artykułu

Total edge irregularity strength of trees

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A total edge-irregular k-labelling ξ:V(G)∪ E(G) → {1,2,...,k} of a graph G is a labelling of vertices and edges of G in such a way that for any different edges e and f their weights wt(e) and wt(f) are distinct. The weight wt(e) of an edge e = xy is the sum of the labels of vertices x and y and the label of the edge e. The minimum k for which a graph G has a total edge-irregular k-labelling is called the total edge irregularity strength of G, tes(G). In this paper we prove that for every tree T of maximum degree Δ on p vertices
tes(T) = max{⎡(p+1)/3⎤,⎡(Δ+1)/2⎤}.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
449-456
Opis fizyczny
Daty
wydano
2006
otrzymano
2005-09-30
poprawiono
2006-01-31
Twórcy
autor
• Institute of Mathematics, P.J. Safarik University, Jesenna 5, SK-041 54 Košice, Slovak Republic
autor
• Institute of Mathematics, P.J. Safarik University, Jesenna 5, SK-041 54 Košice, Slovak Republic
Bibliografia
• [1] M. Aigner and E. Triesch, Irregular assignment of trees and forests, SIAM J. Discrete Math. 3 (1990) 439-449, doi: 10.1137/0403038.
• [2] D. Amar and O. Togni, Irregularity strength of trees, Discrete Math. 190 (1998) 15-38, doi: 10.1016/S0012-365X(98)00112-5.
• [3] M. Bača, S. Jendrol' and M. Miller, On total edge irregular labelling of trees, (submitted).
• [4] M. Bača, S. Jendrol', M. Miller and J. Ryan, On irregular total labellings, Discrete Math. 307 (2007) 1378–1388, doi: 10.1016/j.disc.2005.11.075.
• [5] T. Bohman and D. Kravitz, On the irregularity strength of trees, J. Graph Theory 45 (2004) 241-254, doi: 10.1002/jgt.10158.
• [6] L.A. Cammack, R.H. Schelp and G.C. Schrag, Irregularity strength of full d-ary trees, Congr. Numer. 81 (1991) 113-119.
• [7] G. Chartrand, M.S. Jacobson, J. Lehel, O.R. Oellermann, S. Ruiz and F. Saba, Irregular networks, Congr. Numer. 64 (1988) 187-192.
• [8] A. Frieze, R.J. Gould, M. Karoński and F. Pfender, On graph irregularity strength, J. Graph Theory 41 (2002) 120-137, doi: 10.1002/jgt.10056.
• [9] J.A. Gallian, Graph labeling, The Electronic Jounal of Combinatorics, Dynamic Survey DS6 (October 19, 2003).
• [10] J. Lehel, Facts and quests on degree irregular assignment, in: Graph Theory, Combin. Appl. vol. 2, Y. Alavi, G. Chartrand, O.R. Oellermann and A.J. Schwenk, eds., (John Wiley and Sons, Inc., 1991) 765-782.
• [11] T. Nierhoff, A tight bound on the irregularity strength of graphs, SIAM J. Discrete Math. 13 (2000) 313-323, doi: 10.1137/S0895480196314291.
• [12] W. D. Wallis, Magic Graphs (Birkhäuser Boston, 2001), doi: 10.1007/978-1-4612-0123-6.
Typ dokumentu
Bibliografia
Identyfikatory