Total edge irregularity strength of complete graphs and complete bipartite graphs |
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Authors: | Stanislav Jendrol’ Jozef Miškuf |
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Institution: | Institute of Mathematics, Faculty of Science, University of Pavol Jozef Šafárik, Košice, Slovakia |
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Abstract: | A total edge irregular k-labelling ν of a graph G is a labelling of the vertices and edges of G with labels from the set {1,…,k} in such a way that for any two different edges e and f their weights φ(f) and φ(e) are distinct. Here, the weight of an edge g=uv is φ(g)=ν(g)+ν(u)+ν(v), i. e. the sum of the label of g and the labels of vertices u and v. The minimum k for which the graph G has an edge irregular total k-labelling is called the total edge irregularity strength of G.We have determined the exact value of the total edge irregularity strength of complete graphs and complete bipartite graphs. |
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Keywords: | Irregular labelling Total labelling Complete graphs Complete bipartite graphs Irregularity strength |
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