Journal Article10.7151/DMGT.1133
Strongly multiplicative graphs
Lowell W. Beineke,S. M. Hegde +1 more
63
TL;DR: It is shown that all graphs in some classes, including all trees, are stronglymultiplicative, and the question of the maximum number of edges in a strongly multiplicative graph of a given order is considered.
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Abstract: 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
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Citations
•Journal Article
A Dynamic Survey of Graph Labeling
TL;DR: In this survey I have collected everything I could find on graph labelings techniques that have appeared in journals that are not widely available.
Some new odd harmonious graphs
Samir K. Vaidya,N. H. Shah +1 more
- 18 Aug 2011
TL;DR: In this article, it was shown that the shadow graphs of path Pn and star K1,n are odd harmonious, and that the split graph of path N and star N admits odd harmonic labeling.
31
Prime Cordial Labeling of Some Graphs
Samir K. Vaidya,N. H. Shah +1 more
TL;DR: In this article, it was shown that the split graphs of K1,n and Bn,n are prime cordial graphs and the wheel graph Wn admits prime labeling for n ≥ 8.
Odd Harmonious Labeling of Some Graphs
Samir K. Vaidya,N. H. Shah +1 more
TL;DR: In this article, the shadow graph and splitting graph of bistar Bn,n are odd harmonious graphs and the supersubdivision of path Pn admits odd-harmonious labeling.
Graceful and Odd Graceful Labeling of Some Graphs
Samir K. Vaidya,N. H. Shah +1 more
- 10 Jan 2013
TL;DR: In this paper, it was shown that the square graph of bistar Bn,n, the splitting graph of Bn n,n and the splitting of star K1,n are graceful graphs.
17
References
On Additive Bases and Harmonious Graphs
Ron Graham,Neil J. A. Sloane +1 more
TL;DR: In this paper, the authors considered several types of additive bases and showed that a connected graph with n edges is called harmonious if it is possible to label the vertices with distinct numbers in such a way that the edge sums are also distinct (modulo n).
338
A chronology of the ringel‐kotzig conjecture and the continuing quest to call all trees graceful*
TL;DR: In this paper, the status of the 1963 conjecture of Ringel concerning the decomposition of K, into isomorphs of an arbitrary tree is explained and traced through its modification by Kotzig to the series of attacks intent on proving that trees are graceful.
58
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