Some Results on Skolem Difference Mean Graphs

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 $x\in V$ with distinct elements $f(x)$ from the set$ \lbrace 1,2,3,\ldots ,p+q\rbrace $ in such a way that the edge \textit{e}$ =uv$ is labeled with $ \frac{\vert f(u)-f(v)\vert }{2}$ if $\vert f(u)-f(v)\vert $ is even and $\frac{\vert f(u)-f(v)\vert +1}{2} $ if $\vert f(u)-f(v)\vert $ is odd and the resulting labels of the edges are distinct and are from $\lbrace 1,2,3,\ldots ,q\rbrace $. A graph that admits skolem difference mean labeling is called a skolem difference mean graph. In this paper, the author studied some results on skolem difference mean graphs.