https://doi.org/10.65770/NRFM2043
Abstract
In this article, the concept of 2-Skolem difference mean labeling, relaxed 2-Skolem difference mean labeling, and 2-Skolem difference mean number of a graph are introduced. A graph G=(V,E) with p vertices and 2q edges is said to have 2-Skolem difference mean labeling if it is possible to label the vertices x∈V with distinct elements f(x) from the set {1,2,…,p} in such a way that the edge e=uv is labelled 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 {1,1,2,2,3,3,…q,q}. A graph that admits 2-Skolem difference mean labeling is called a 2-Skolem difference mean graph. The authors studied 2-Skolem difference mean labeling of some graphs.
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