ABSTRACT
The nth tetrahedral number is denoted by ππ and is of the form ππ = 1/6π (π+1) (π+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) β{0, 2, 4, . . . , 2ππ-2 , 2ππ} such that the induced edge function πβ: E(G) β{π1,π2 , . . . ,ππ} defined by πβ(uv) = (π(π’)+ π(π£))/2 β e=uvβE(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, ππ @ ππ, banana tree, Y- tree and F-tree are even vertex tetrahedral mean graphs.
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