Strongly Prime Labeling For Some Graphs

Abstract

A graph $G=(V,E)$ with $\, n$ vertices is said to admit prime labeling if its vertices can be labeled with distinct positive integers not exceeding, n such that the label of each pair of adjacent vertices are relatively prime. A graph $G$ which admits prime labeling is called a prime graph and a graph $G$ is said to be a strongly prime graph if for any vertex, $v$ of $G$ there exists a prime labeling, f satisfying, $f\left(v\right)=1$. In this paper we prove that the graphs corona of triangular snake, corona of quadrilateral snake, corona of ladder graph and a graph obtained by attaching $P_{2}$ at each vertex of outer cycle of prism $D_{n}$ by $(D_{n} ;P_{2})$, helm, gearwheel are strongly prime graphs.