ON RADIO ANALYTIC MEAN D-DISTANCE NUMBER OF MORE GRAPHS

A Radio Analytic Mean D-distance labeling of associated diagram $G$ is a balanced guide $v$ from the vertex set $V(G)$ to $N$ such that for two distinct vertices $u$ and $v$ of $G$. $d^D\left(u,v\right) +\left\lceil \frac{\left|f({u)}^2-f(v)^2\right|}{2}\right\rceil \ge 1+\ {diam}^{D\ }(G)$.

Some Results on Prime and Distinct Prime Distance Labeling of Graphs

Let be the set of all integers. A graph is a prime distance graph if there exists an injective function such that for any two adjacent vertices and , the integer is a prime. So is a prime distance graph if and only if there exists a prime distance labeling of . If the edge labels of are also distinct, then is called a distinct prime distance labeling of and is called a distinct prime distance graph. The generalized Petersen graphs are defined to be a graph on vertices with and , subscripts modulo . In this paper, we show that the generalized Petersen graphs permit a prime distance labeling for all even and conjecture that and admit a prime distance labeling for any and all odd , respectively. We also prove that the cycle admits a distinct prime distance labeling for all , besides establishing the prime distance labeling for some graphs.