Extra Skolem Difference Mean Labeling of Some Graphs

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.