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Proof Let u l m v l m l l , , , 1 1 1 ≤ ≤ ≤ ≤ − { } be the vertices and a b c l m l l l , , , 1 1 ≤ ≤ − { } be the edges which are denoted as in Figure 2.1. First we label the vertices: For 1 1 3 3 ≤ ≤ − = + − l m f v k l l ( ) For 1 3 4 ≤ ≤ = + − l m f u k l l ( ) Then the induced edge labels are: f a k * 1 2 ( )= + For 2 1 3 2 1 1 ≤ ≤ − ( )= + − ( )= + l m f a k l f c k l * * f c k l l * ( )= + − 3 1

k-Contra Harmonic Mean Labeling of Snake Related Graphs