On Super Mean Labeling for Total Graph of Path and Cycle

• Main Authors: Nur Inayah, I. Wayan Sudarsana, Selvy Musdalifah, Nurhasanah Daeng Mangesa
• Format: Article
• Language: English
• Published: Hindawi Limited 2018-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Online Access: http://dx.doi.org/10.1155/2018/9250424

Let G(V,E) be a graph with the vertex set V and the edge set E, respectively. By a graph G=(V,E) we mean a finite undirected graph with neither loops nor multiple edges. The number of vertices of G is called order of G and it is denoted by p. Let G be a (p,q) graph. A super mean graph on G is an injection f:V→{1,2,3…,p+q} such that, for each edge e=uv in E labeled by f⁎e=fu+f(v)/2, the set fV∪{f⁎e:e∈E} forms 1,2,3,…,p+q. A graph which admits super mean labeling is called super mean graph. The total graph T(G) of G is the graph with the vertex set V∪E and two vertices are adjacent whenever they are either adjacent or incident in G. We have showed that graphs T(Pn) and TCn are super mean, where Pn is a path on n vertices and Cn is a cycle on n vertices.