An Application on Harmonic Mean Labeling of Variations in Triangular Snake Graphs

Abstract

A graph G with p vertices and q edges is called a harmonic mean(HM) labeling if it is possible to label the vertices x∈v with distinct labels ρ(x) from {1,2,⋯,q+1} in such a way that each edge e=ab is labeled with ρ(ab)=⌈(2ρ(a)ρ(b))/(ρ(a)+ρ(b))⌉ or ⌊(2ρ(a)ρ(b))/(ρ(a)+ρ(b))⌋ then the edge labels are distinct.
In this case ρ is called Harmonic mean(HM) labeling of G. In this paper we introduce new graphs obtained from triangular snake graph TS_n such as TS_n∘K_1, and prove that they are Harmonic Mean labeling graphs.