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In this paper, the connected three star graph G = K 1 , ϕ 1 ∧ K 1 , ϕ 2 ∧ K 1 , ϕ 3 is a skolem mean like graph if and only if | ϕ 2 − ϕ 3 | ≤ ϕ 1 + 4 and ϕ 1 + ϕ 2 + 4 ≤ ϕ 3 ≤ ϕ 1 + ϕ 2 − 2 , where ϕ 1 = 1 , 2 , 3… , ϕ 2 = 1 , 2 , 3 , … . with the condition ϕ 1 ≤ ϕ 2 < ϕ 3 is proved. 2010 Mathematical Subject Classification Number: 05C78

A new labeling named ‘Sum Modulo Three’ (SMT) is introduced and its verifications on a general single star and general two star are provided. Also an application using the labeling on a general two star is presented.

In this paper, we have found a technique for coding a secret messages by applying the skolem mean like labeling on the two star graph K 1,φ Λ K 1,π for two different cases π = φ+1 and π = φ+4 using AMGL (Alphabets maneuvered Graph Labeling) code. We provided two illustrations for converting plain text into cipher text (picture coding) and method for labeling the skolem mean like graph is described.