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On Bounds for the Product Irregularity Strength of Graphs.
- Source :
- Graphs & Combinatorics; Sep2015, Vol. 31 Issue 5, p1347-1357, 11p
- Publication Year :
- 2015
-
Abstract
- For a graph $$X$$ with at most one isolated vertex and without isolated edges, a product-irregular labeling $$\omega :E(X)\rightarrow \{1,2,\ldots ,s\}$$ , first defined by Anholcer in 2009, is a labeling of the edges of $$X$$ such that for any two distinct vertices $$u$$ and $$v$$ of $$X$$ the product of labels of the edges incident with $$u$$ is different from the product of labels of the edges incident with $$v$$ . The minimal $$s$$ for which there exist a product irregular labeling is called the product irregularity strength of $$X$$ and is denoted by $$ps(X)$$ . In this paper it is proved that $$ps(X)\le |V(X)|-1$$ for any graph $$X$$ with more than $$3$$ vertices. Moreover, the connection between the product irregularity strength and the multidimensional multiplication table problem is given, which is especially expressed in the case of the complete multipartite graphs. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09110119
- Volume :
- 31
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Graphs & Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 109077664
- Full Text :
- https://doi.org/10.1007/s00373-014-1458-5