Strongly multiplicative graphs

• Autorzy: L.W. Beineke , S.M. Hegde
• Języki publikacji: EN

Abstrakty

EN

A graph with p vertices is said to be strongly multiplicative if its vertices can be labelled 1,2,...,p so that the values on the edges, obtained as the product of the labels of their end vertices, are all distinct. In this paper, we study structural properties of strongly multiplicative graphs. We show that all graphs in some classes, including all trees, are strongly multiplicative, and consider the question of the maximum number of edges in a strongly multiplicative graph of a given order.

Słowa kluczowe

EN

graph labelling; multiplicative labelling

Kategorie tematyczne

• 05C78: Graph labelling (graceful graphs, bandwidth, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2001
• Tom: 21
• Numer: 1
• Strony: 63-75

Daty

wydano

2001

otrzymano

2000-08-09

Twórcy

autor

L.W. Beineke

• Indiana University-Purdue University, Fort Wayne, Indiana 46805, USA

autor

S.M. Hegde

• Karnataka Regional Engineering College, Srinivasnagar, Karnataka - 574157, India

Bibliografia

• [1] B.D. Acharya and S.M. Hegde, On certain vertex valuations of a graph, Indian J. Pure Appl. Math. 22 (1991) 553-560.
• [2] G.S. Bloom, A chronology of the Ringel-Kotzig conjecture and the continuing quest to call all trees graceful, Ann. N.Y. Acad. Sci. 326 (1979) 32-51, doi: 10.1111/j.1749-6632.1979.tb17766.x.
• [3] F.R.K. Chung, Labelings of graphs, Selected Topics in Graph Theory 3 (Academic Press, 1988) 151-168.
• [4] P. Erdős, An asymptotic inequality in the theory of numbers, Vestnik Leningrad. Univ. 15 (1960) 41-49.
• [5] J.A. Gallian, A dynamic survey of graph labeling, Electronic J. Comb. 5 (1998) #DS6.
• [6] R.L. Graham and N.J.A. Sloane, On additive bases and harmonious graphs, SIAM J. Algebraic Discrete Methods 1 (1980) 382-404, doi: 10.1137/0601045.
• [7] A. Rosa, On certain valuations of the vertices of a graph, in: Theory of Graphs, Internat. Symposium, Rome, July 1966 (Gordon and Breach, Dunod, 1967) 349-355.

Identyfikatory

DOI

10.7151/dmgt.1133