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2010 | 30 | 4 | 539-544
Tytuł artykułu

Arithmetic labelings and geometric labelings of countable graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An injective map from the vertex set of a graph G-its order may not be finite-to the set of all natural numbers is called an arithmetic (a geometric) labeling of G if the map from the edge set which assigns to each edge the sum (product) of the numbers assigned to its ends by the former map, is injective and the range of the latter map forms an arithmetic (a geometric) progression. A graph is called arithmetic (geometric) if it admits an arithmetic (a geometric) labeling. In this article, we show that the two notions just mentioned are equivalent-i.e., a graph is arithmetic if and only if it is geometric.
Wydawca
Rocznik
Tom
30
Numer
4
Strony
539-544
Opis fizyczny
Daty
wydano
2010
otrzymano
2009-02-14
poprawiono
2009-10-19
zaakceptowano
2009-10-20
Twórcy
  • School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India
Bibliografia
  • [1] B.D. Acharya and S.M. Hegde, Arithmetic graphs, J. Graph Theory 14 (1990) 275-299, doi: 10.1002/jgt.3190140302.
  • [2] B.D. Acharya and S.M. Hegde, On certain vertex valuations of a graph, Indian J. Pure and Appl. Math. 22 (1991) 553-560.
  • [3] L.W. Beineke and S.M. Hegde, Strongly multiplicative graphs, Discuss. Math. Graph Theory 21 (2001) 63-75, doi: 10.7151/dmgt.1133.
  • [4] S.M. Hegde, On multiplicative labelings of a graph, J. Combin. Math. and Combin. Comp. 65 (2008) 181-195.
  • [5] S.M. Hegde and P. Shankaran, Geometric labeled graphs, AKCE International J. Graphs and Combin. 5 (2008) 83-97.
  • [6] G.R. Vijayakumar, Arithmetic labelings and geometric labelings of finite graphs, J. Combin. Math. and Combin. Comp. (to be published).
  • [7] D.B. West, Introduction to Graph Theory, Second edition (Printice Hall, New Jersey, USA, 2001).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1511
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