Odd Prime Labeling of Graphs Related to Circular Ladder

Abstract

In a graph \(G\) with point set \(V\) a mapping $f$ is said to be an odd prime labeling if \(f\) is a one-to-one function from point set \(V\) to \({\{1,3,5,2|V|-1}\}\) satisfying the condition that for each line \(uv\) in \(G\) the greatest common divisor of the labels of the end points \(f(u),f(v)\) is one. Investigated in this paper the odd prime labeling of circular ladder related graphs and we prove that the graphs such as \(CL(n)\), \(SCL(n)\), \(CL(n)\bigodot K_{1}\), \(CL(n)\bigodot \bar{K}_{2}\), \(CL(n) \bigodot\bar{K}_{3}\) are all odd prime graphs.