**ABSTRACT**

The nth tetrahedral number is denoted by 𝑇𝑛 and is of the form 𝑇𝑛 = 1/6𝑛 (𝑛+1) (𝑛+2). A graph G with p vertices and q edges is said to have an even vertex tetrahedral mean labeling if there exists an injective function f: V(G) →{0, 2, 4, . . . , 2𝑇𝑞-2 , 2𝑇𝑞} such that the induced edge function 𝑓∗: E(G) →{𝑇1,𝑇2 , . . . ,𝑇𝑞} defined by 𝑓∗(uv) = (𝑓(𝑢)+ 𝑓(𝑣))/2 ∀ e=uv∈E(G) is a bijection. A graph which admits even vertex tetrahedral mean labeling is called an even vertex tetrahedral mean graph. In this paper, we introduce even vertex tetrahedral mean labeling and we prove that path, star, bistar, coconut tree, caterpillar, shrub, 𝑃𝑚 @ 𝑃𝑛, banana tree, Y- tree and F-tree are even vertex tetrahedral mean graphs.

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