The Construction of Labeling and Total Irregularity Strength of Specified Caterpillar Graph

[摘要] Let G be a simple, connected and undirected graph with vertex set V and edge set E. A total k-labeling f : V ∪ E → {1, 2, , k} is defined as totally irregular total k-labeling if the weights of any two different both vertices and edges are distinct. The weight of vertex x is defined as wt(x) = f(x) + ∑xy∈Ef(xy), while the weight of edge xy is wt(xy) = f(x) + f(xy) + f(y). A minimum k for which G has totally irregular total k-labeling is mentioned as total irregularity strength of G and denoted by ts(G). This paper contains investigation of totally irregular total k-labeling for caterpillar graphs Sn,2,mand determination of their total irregularity strengths. In addition, the total vertex and total edge irregularity strength of this graph also be determined. The results are tvs(Sn;2;m) = ⌈n+m-1/2⌉, tes(Sn;2;m) =⌈n+m+2/3⌉ and ts(Sn;2;m) = ⌈n+m-1/2⌉for n, m ≥ 3.

[发布机构] Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Surakarta, Indonesia^1

[效力级别] 教育 [学科分类] 发展心理学和教育心理学

[关键词] Caterpillar graphs;Edge-sets;Irregularity strength;Undirected graph;Vertex set