Abstract
A toted vertex irregular k-labeling φ of a graph G is a labeling of the vertices and edges of G with labels from the set {1,2,...,k} in such a way that for any two different vertices x and y their weights wt(x) and wt(y) are distinct. Here,the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x. The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G. We have determined an exact value of the total vertex irregularity strength of cartesian and categorical product of two paths of given length.
Original language | English |
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Pages (from-to) | 239-249 |
Number of pages | 11 |
Journal | Utilitas Mathematica |
Volume | 90 |
Publication status | Published - Mar 2013 |
Externally published | Yes |
Keywords
- Cartesian products
- Categorical product
- Paths
- Total vertex irregularity strength
- Vertex irregular total k-labeling
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics