Graph labeling is an important area of research in Graph theory. There are many kinds of graph labeling such as Graceful labeling, Magic labeling, Prime labeling, and other different labeling techniques.In this paper the Prime labeling of certain classes of graphs are discussed.It is of interest to note that H-graph which is a 3 –regular graph satisfy Prime labeling. A Gear graph is a graph obt...

A graph Γ=(V,E) of order n is distance magic if it admits a bijective labeling ℓ:V→{1,2,…,n} its vertices for which there exists positive integer κ such that ∑u∈N(v)ℓ(u)=κ all v∈V, where N(v) the neighborhood v. circulant admitting an automorphism cyclically permuting vertices. In this paper we study circulants valency 6. We obtain some necessary and sufficient conditions 6 to be magic, thereby...

In this paper, we consider a strongly repelling model of $n$ ordered particles $\{e^{i \theta_j}\}_{j=0}^{n-1}$ with the density $p({\theta_0},\dots, \theta_{n-1})=\frac{1}{Z_n} \exp \big\{-\frac{\beta}{2}\sum_{j \ne k} \sin^{-2} \big( \frac{\theta_j-\theta_k}{2}\big)\big\}$, $\beta>0$. Let $\theta_j=2 \pi j/n+x_j/n^2+{const}$ such that $\sum_{j=0}^{n-1}x_j=0$. Define $\zeta_n (2 j/n) =x_j/\sqr...

Let $P$ be a complex polynomial of the form $P(z)=zdisplaystyleprod_{k=1}^{n-1}(z-z_{k})$,where $|z_k|ge 1,1le kle n-1$ then $ P^prime(z)ne 0$. If $|z|

We establish the existence of vertex-magic total labelings (VMTLs) for several infinite classes of regular graphs. The main method of construction is to assemble a number of appropriately labeled copies of one graph into a single graph with a VMTL. This method enables us for example to begin with any even-regular graph and from it construct a cubic graph possessing a VMTL. An important feature ...