Generating Skolem Difference Mean 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 V with distinct elements f(x) from {1,2,….,p+q} in such a way that the edge e = uv is labeledwith |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 edges get distinct labels from {1,2,…,q}. A graph that admits skolem difference mean labeling is called a Skolem difference mean graph A graph G = (V, E) with p vertices and q edges is said to have Near skolem difference mean labeling if it is possible to label the vertices x V with distinct elements f(x) from {1,2,….,p+q-1,p+q+2} in such a way that each edge e = uv, is labeled as f*(e) = |f(u)-f(v)|/2 if |f(u)-f(v)| is even and f*(e) =(|f(u)-f(v)|+1)/2 if |f(u)-f(v)| is odd. The resulting labels of the edges are distinct and from {1,2,…,q}. A graph that admits a Near skolem difference mean labeling is called a Near Skolem difference mean graph. In this paper, the authors generate skolem difference mean graphs from near skolem difference mean graphs.