**ABSTRACT**

A graph G =(𝑉,𝐸) with p vertices and q edges is said to have skolem difference mean labeling if it is possible to label the vertices x 𝜖 𝑉 with distinct elements f (𝑥) from the set {1,2…𝑝+𝑞} in such a way that the edge e =𝑢𝑣 is labeled with (|𝑓(𝑢)−𝑓(𝑣)|)/2 if |𝑓(𝑢)−𝑓(𝑣)| is even and (|𝑓(𝑢)−𝑓(𝑣)|+1)/2 if |𝑓(𝑢)−𝑓(𝑣)| is odd and the resulting labels of the edges are distinct and are from {1,2…𝑞}. A graph that admits skolem difference mean labeling is called a skolem difference mean graph. If one of the skolem difference mean labeling of G satisfies the condition that all the labels of the vertices are odd, then we call this skolem difference mean labeling an extra skolem difference mean labeling and call the graph G an extra skolem difference mean graph. In this paper, extra skolem difference mean labeling of some graphs are studied.

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