R-Harmonic Mean Labeling of Graphs

C. David Raj

Department of Mathematics, Malankara Catholic College, Mariagiri, Kaliyakkavilai, Kanyakumari 629153, Tamil Nadu, INDIA.


In this paper, I introduce new labeling techniques called R-Harmonic mean labeling. A graph G with p vertices and q edges is called a R-Harmonic mean graph if there is a function 𝜏 from the vertex set of G to {0, 1, 2, 3, , q} with 𝜏 is one-one and 𝜏 induces a bijection 𝜏* from the edge set of G to {1, 2, 3, , q}, where 𝜏*(e = uv) ={⌈2𝜏(𝑢)𝜏 (v𝜏(𝑢)+ 𝜏 (v)⌉ 𝑖𝑓 𝜏(𝑢)≠0 𝑎𝑛𝑑 𝜏(v)≠01 otherwise and the function 𝜏 is called as R-Harmonic mean labeling of G. Further I investigate some of R-Harmonic mean graphs.

Keywords :Graph, Harmonic mean labeling, Harmonic mean graph, R-Harmonic mean labeling and R-Harmonic mean graph.

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