Abstract A binary vertex labeling f : V (G) → Z2 of a graph G is said to be friendly if the number of vertices labeled 0 is almost the same as the number of vertices labeled 1. This friendly labeling induces an edge labeling f∗ : E(G) → Z2 defined by f∗(uv) = f(u)f(v) for all uv ∈ E(G). Let ef (i) = {uv ∈ E(G) : f∗(uv) = i} be the number of edges of G that are labeled i. Productcordial index of...

In this paper we present an algorithm and prove the existence of graph labelings such as Z 3 -magic, Cordial, total cordial, E-cordial, total E-cordial, Product cordial, total product cordial, Product E-cordial, total product E-cordial labelings for the Competition graph of the Cayley digraphs associated with the diheadral group D n . AMS SUBJECT CLASSIFICATION: 05C78.

A graph G(V,E) with vertex set V is said to have a prime labeling if its vertices are labeled with distinct integers 1, 2, . . . , |V | such that for each edge xy ∈ E the labels assigned to x and y are relatively prime. A prime cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, . . . , |V |} such that if each edge uv is assigned the label 1 if gcd(f(u), f(v)) = 1 ...

A graph G = (V,E) with p vertices and q edges is said to be a Total Mean Cordial graph if there exists a function f : V (G) → {0, 1, 2} such that for each edge xy assign the label ⌈ f(x)+f(y) 2 ⌉ where x, y ∈ V (G), and the total number of 0, 1 and 2 are balanced. That is |evf (i)− evf (j)| ≤ 1, i, j ∈ {0, 1, 2} where evf (x) denotes the total number of vertices and edges labeled with x (x = 0,...