A graph G= (V,E) with p vertices and q edges is called a Harmonic mean graph if it is possible to label the vertices xV with distinct labels f(x) from 1,2,....,q+1 in such a way that when each edge e=uv is labeled with f(uv)= ( ) ( ) ( ) ( ) (or) ( ) ( ) ( ) ( ) , then the edge labels are distinct. In this case, f is called Harmonic mean labeling of G. In this paper we prove that Double Triang...

In this paper we introduce a new type of labeling known as even vertex odd mean labeling. A graph G with p vertices and q edges is said to have an even vertex odd mean labeling if there exists an injective function f : V (G) → {0, 2, 4, . . . , 2q−2, 2q} such that the induced map f∗ : E(G) → {1, 3, 5, . . . , 2q− 1} defined by f∗(uv) = f(u)+f(v) 2 is a bijection. A graph that admits an even ver...

Let G = (V,E) be a graph with p vertices and q edges. G is said to have skolem difference mean labeling if it is possible to label the vertices x ∈ V with distinct elements f(x) from 1, 2, 3, ..., p+ q in such a way that for each edge e = uv, let f∗(e) = l |f(u)−f(v)| 2 m and the resulting labels of the edges are distinct and are from 1, 2, 3, ..., q. A graph that admits a skolem difference mea...

In this paper, we introduce a new labeling called one modulo three mean labeling. A graph G is said to be one modulo three mean graph if there is an injective function φ from the vertex set of G to the set {a | 0 ≤ a ≤ 3q2 and either a≡0(mod 3) or a≡1(mod 3) } where q is the number of edges of G and φ induces a bijection φ * from the edge set of G to { } |1 3 2 and ( 3) a a q a 1 mod ≤ ≤ − ≡ gi...

Consider a graph G with |V (G)| = p and |E(G)| q let f : V (G) → {k, k + 1, 2, . − 1}} be an injective function. The induced edge labeling ∗ for vertex is defined by (e) all e uv ∈ E(G) bijective. If f(V (G)) ∪ {f E(G)} , 1}, then called k-super cube root mean labeling. such exists, graph. In this paper, I introduce prove the existence of to graphs viz., triangular snake Tn, double D(Tn), Quadr...