Vertex \(k\)-Prime Labeling of Cyclic Snakes

On Odd Graceful Labeling of the Generalization of Cyclic Snakes

The objective of this paper is to present a new class of odd graceful graphs. In particular, we show that the linear cyclic snakes (1, k) C4snake and (2, k) C4snake are odd graceful. We prove that the linear cyclic snakes (1, k) C6snake and (2, k) C6snake are odd graceful. We also prove that the linear cyclic snakes (1, k) C8snake and (2, k) C8snake are odd graceful. We generalize the above res...

PD-prime cordial labeling of graphs

vspace{0.2cm} Let $G$ be a graph and $f:V(G)rightarrow {1,2,3,.....left|V(G)right|}$ be a bijection. Let $p_{uv}=f(u)f(v)$ and\ $ d_{uv}= begin{cases} left[frac{f(u)}{f(v)}right] ~~if~~ f(u) geq f(v)\ \ left[frac{f(v)}{f(u)}right] ~~if~~ f(v) geq f(u)\ end{cases} $\ for all edge $uv in E(G)$. For each edge $uv$ assign the label $1$ if $gcd (p_{u...

Vertex Equitable Labeling of Double Alternate Snake Graphs

Let G be a graph with p vertices and q edges and A = {0, 1, 2, . . . , [q/2]}. A vertex labeling f : V (G) → A induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. For a ∈ A, let vf (a) be the number of vertices v with f(v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, |vf (a) − vf (b)| ≤ 1 and the indu...

k-equitable mean labeling

Prime Labeling of Grids

A labeling f on a graph G on n vertices is called a prime labeling if f is a bijection from the vertex set V (G) to {1, 2, · · · , n} such that f(x) and f(y) are coprime if x and y are adjacent. It was shown by Sundaram et al. [1] that the planar grid Pm × Pn has a prime labeling if m ≤ n and n is a prime. In this paper it is proved that the following grids have a prime labeling: (i) Pn+1 × Pn+...