Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4649046 | Discrete Mathematics | 2010 | 6 Pages |
Abstract
A vertex irregular total kk-labelling λ:V(G)∪E(G)⟶{1,2,…,k}λ:V(G)∪E(G)⟶{1,2,…,k} of a graph GG is a labelling of vertices and edges of GG done in such a way that for any different vertices xx and yy, their weights wt(x)wt(x) and wt(y)wt(y) are distinct. The weight wt(x)wt(x) of a vertex xx is the sum of the label of xx and the labels of all edges incident with xx. The minimum kk for which a graph GG has a vertex irregular total kk-labelling is called the total vertex irregularity strength of GG, denoted by tvs(G). In this paper, we determine the total vertex irregularity strength of trees.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Nurdin, E.T. Baskoro, A.N.M. Salman, N.N. Gaos,