In this paper we prove that the extended triplicate graph (ETG) of finite paths admits product E-cordial, total product E-cordial labelings. We show that ETG of finite paths of length n where n ∉ {4m-3|m∈N} admits E-Cordial, total E-cordial labelings and also we prove the existence of Z3 – magic labeling for the modified Extended Triplicate graph.

For any integer k > 0, a tree T is k-cordial if there exists a labeling of the vertices of T by Zk, inducing edge-weights as the sum modulo k of the labels on incident vertices to a given edge, which furthermore satisfies the following conditions: 1. Each label appears on at most one more vertex than any other label. 2. Each edge-weight appears on at most one more edge than any other edge-weigh...

let g be a (p, q) graph. let f : v (g) → {1, 2, . . . , k} be a map. for each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of g if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....

In this paper we discuss cordial labeling in the context of arbitrary supersubdivision of graph. We prove that the graphs obtained by arbitrary supersubdivision of path as well as star admit cordial labeling. In addition to this we prove that the graph obtained by arbitrary supersubdivision of cycle is cordial except when n and all mi are simultaneously odd numbers. Mathematics Subject Classifi...

Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a function. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if ∣∣vf (i)− vf (j)∣∣ 6 1, i, j ∈ {1, 2, . . . , k} and ∣∣ef (0)− ef (1)∣∣ 6 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled ...

A divisor cordial labeling of a graph G with vertex set V vertex G is a bijection f from V to {1, 2, 3, . . . |V|} such that an edge uv is assigned the label 1 if f(u) divides f(v) or f(v)divides f(u) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a divisor cordial labeling, then it is called divisor cordial gr...

Let G be a (p, q) graph. Let f : V (G) → {1, 2 . . . , p} be a function. For each edge uv, assign the label |f (u)− f (v)|. f is called a difference cordial labeling if f is a one to one map and |ef (0)− ef (1)| ≤ 1 where ef (1) and ef (0) denote the number of edges labeled with 1 and not labeled with 1 respectively. A graph with a difference cordial labeling is called a difference cordial grap...

A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,... | |} V such that an edge uv is assigned the label 1 if either ( ) | ( ) f u f v or ( ) | ( ) f v f u and the label 0 if ( ) ( ) f u f v , then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a divisor cordial labeling is called a divisor cordial ...

We extend the de nition of edge-cordial graphs due to Ng and Lee for graphs on 4k, 4k+1, and 4k+3 vertices to include graphs on 4k+2 vertices, and show that, in fact, all graphs without isolated vertices are edge-cordial. Ng and Lee conjectured that all trees on 4k, 4k + 1, or 4k + 3 vertices are edge-cordial. Intuitively speaking, a graph G is said to be edge-cordial if its edges can be labell...

a graph g is said to have a totally magic cordial labeling with constant c if there exists a mapping f : v (g) ∪ e(g) → {0, 1} such that f(a) + f(b) + f(ab) ≡ c (mod 2) for all ab ∈ e(g) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. in this paper, we give a necessary condition for an odd graph to be not totally magic cordial and ...