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 ∈ 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)|+12 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)|+12 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.
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