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In this paper, we investigate the pair mean cordial labeling behavior of udukkai graph, octopus graph, double wheel graph, barbell graph, drum graph, vanessa graph and fire cracker graph. [ABSTRACT FROM AUTHOR]

In this paper we investigate the pair difference cordial labeling behaviour of some product related graphs. [ABSTRACT FROM AUTHOR]

In this paper we determine the pair difference cordial number of degree splitting graph of bistar, complete bipartite graph, ladder, wheel. [ABSTRACT FROM AUTHOR]

Let a graph G = (V, E) be a (p, q) graph. Define ρ = {p/2, p is even p - 1/2, p is odd, and M = {±1, ±2, ⋯ ± ρ} called the set of labels. Consider a mapping λ : V → by assigning different labels in M to the different elements of V when p is even and different labels in M to p -- 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling λ(2)+λ(v)/2 if λ(2) + λ(v) is even and λ(u)+λ(v)+1/2 if λ(u) + λ(v) is odd such that ... ≤ where ... and ... respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G with a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we discuss here the pair mean cordial labeling of union graphs like Lm, υ Ln, Pm υ Ln, Cm Ln, Wm υ υ Ln, Sm υ Ln. [ABSTRACT FROM AUTHOR]

Let G be a graph. Let f : V (G) → {0, 1, 2, . . ., k -- 1} be a function where k ∈ N and k > 1. For each edge uv, assign the label f (uv) = [f(u)+f(v)/2]. f is called a k-total mean cordial labeling of G if |tmf (i) -- tmf (j)| ≤ 1, for all i, j ∈ {0, 1, 2, . . ., k -- 1}, where tmf (x) denotes the total number of vertices and edges labelled with x, x ∈ {0, 1, 2, . . ., k -- 1}. A graph with admit a k-total mean cordial labeling is called k-total mean cordial graph. In this paper we examine the 4-Total mean cordial labeling of some trees. [ABSTRACT FROM AUTHOR]

Let G be a graph. Let f: V (G) → {0,1, 2, ..., k -- 1} be ai function where k ... N and k > 1. For each edge uv, assign the label f (uv) = f(u)+f (v) ~∣. f is called ktotal mean cordial labeling of G if |tmf (i) -- tmf (j)| ≤ 1, for all i, j ... {0, 1, . . ., k -- 1}, where tmf (x) denotes the total number of vertices and edges labelled with x, x ... {0,1,2, ..., k -- 1}. A graph with admit a k-total mean cordial labeling is called k-total mean cordial graph. [ABSTRACT FROM AUTHOR]

Let G be a graph and let f: V (G) ! f0; 1; 2;; k 1g be a function where k 2 N and k > 1. For each edge uv, assign a label f (uv) = l f(u)+f(v) 2 m and f is called a k-total mean cordial labeling of G if jtmf (i) tmf (j)j 1 for all i; j 2 f0; 1;; k 1g, where tmf (x) denotes the total number of vertices and edges la-belled with x, x 2 f0; 1; 2;; k 1g. A graph with admit a k-total mean cordial labeling is called k-total mean cordial graph. In this paper we investigate the 4-total mean cordial labeling behavior of some graphs which are obtained from stars. [ABSTRACT FROM AUTHOR]

In this paper we investigate the pair difference cordial labeling behaviour of double cone, double step grid, sun ower, shell graph and double arrow graph. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the pair difference cordial labeling behaviour of some star related graphs. [ABSTRACT FROM AUTHOR]

Let G be a graph. Let f : V (G) → {0, 1, 2, . . ., k − 1} be a function where k ∈ N and k > 1. For each edge uv, assign the label f (uv) = ᒥ f (u) + f (v)/2 ⏋and f is called a k-total mean cordial labeling of G if |tmf (i) − tmf (j)| ≤ 1, for all i, j ∈ {0, 1, 2, . . ., k − 1}, where tmf (x) denotes the total number of vertices and edges labelled with x, x ∈ {0, 1, 2, . . ., k − 1}. A graph with admit a k-total mean cordial labeling is called k-total mean cordial graph. In this paper we investigate the 4-Total mean cordial labeling behavior of some graphs like C4 × Pn, middle graph of Pn, total graph of Pn, middle graph of Cn, total graph of Cn and kayak paddale graph. [ABSTRACT FROM AUTHOR]

In this paper we study the pair difference cordial labeling behavior of some trees and some graphs derived from cube graph. [ABSTRACT FROM AUTHOR]

In this paper, we discuss about the pair difference cordial labeling behavior of subdivision of wheel and comb graphs. [ABSTRACT FROM AUTHOR]

Let G = (V, E) be a (p, q) graph. Define if p is even if p is odd and L = {±1, ±2, ±3, ∙∙∙, ±ρ} called the set of labels. Consider a mapping f: V--→ L by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f (u) -- f (v)| such that ∣Δf1 -- Δf c ∣ ≤ 1, where Δf1 and Δfc respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of Pair Difference Cordial Labeling of Franklin graph, Heawood graph, Tietze graph and Durer graph. [ABSTRACT FROM AUTHOR]

Let G be a graph. Let f : V (G) → {0, 1, 2, ..., k -- 1} be a function where k ∈ ℕ and k > 1. For each edge uv, assign the label f (uv) = [f(u)+f(v)/2]. f is called k-total mean cordial labeling of G if |tmf (i) -- tmf (j)| ≤ 1 for all i, j ∈ {0, 1, 2, ⋯, k --1} where tmf (x) denotes the total number of vertices and edges labelled with x, x ∈ {0, 1, 2, ⋯, k -- 1}. A raph with admit a k-total mean cordial labeling is called k-total mean cordial graph. [ABSTRACT FROM AUTHOR]

Let G be a(p, q) graph. Let f be a map from V(G) to {1, 2, ..., p}. For each edge xy, assign the label [absolute value of f(x) - f(y)]. f is called a difference cordial labeling if f is a one to one map and [absolute value of [e.sub.f](0) - [e.sub.f](1)] ≤ 1 where [e.sub.f](1) and [e.sub.f](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 graph. In this paper we investigate the difference cordial labeling behavior of subdivision of some graphs. Keywords Subdivision, web, wheel, book, corona. 2000 Mathematics Subject Classification: 05C78, §1. Introduction and preliminaries Let G = (V, E) be (p, q) graph. In this paper we have considered only simple and undirected graphs. The number of vertices of G [...]

Let G be a (p; q) graph. Let f be a map from V (G) to the set {1, 2, . . .; kg where k is an integer 2 < k ≤ jV (G)j. For each edge uv assign the label r where r is the remainder when f(u) is divided by f(v) (or) f(v) is divided by f(u) according as f(u) ≥ f(v) or f(v) ≥ f(u). The function f is called a k-remainder cordial labeling of G if |vf (i) - vf (j)j ≤ 1, i; | 2 f1; . . .; kg where vf (x) denote the number of vertices labelled with x and |no - ne} ≤ 1 where ne and no respectively denote the number of edges labeled with even integers and number of edges labelled with odd integers. A graph with a k-remainder cordial labeling is called a k- remainder cordial graph. In this paper we investigate the 4-remainder cordial labeling behavior of parachute, twig and kayak paddale graph. [ABSTRACT FROM AUTHOR]

Let G be a (p, q) graph. Let f be a map from V (G) to the set {1, 2, · · ·, k} where k is an integer 2 < k ≤ |V (G)|. For each edge uv assign the label r where r is the remainder when f(u) is divided by f(v) (or) f(v) is divided by f(u) according as f(u) ≥ f(v) or f(v) ≥ f(u). The function f is called a k-remainder cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, · · ·, k} where vf (x) denote the number of vertices labelled with x and |ηo − ηe| ≤ 1 where ηe and ηo respectively denote the number of edges labeled with even integers and number of edges labelled with odd integers. A graph with a k-remainder cordial labeling is called a k-remainder cordial graph. In this paper we investigate the 4−remainder cordial labeling behavior of banana tree, coconut tree, bamboo tree. [ABSTRACT FROM AUTHOR]

In this paper we investigate the 4-difference cordial labeling behaviour of jelly fish, jewel graph, comb, subdivision of star, subdivision of bistar, book with triangle pages. [ABSTRACT FROM AUTHOR]

Let G be a graph. Let f : V (G) → {0; 1; 2; ⋯, k - 1} be a map where k ∈ ℕ and k > 1. For each edge uv, assign the label |f(u) - f(v)|. f is called k-total difference cordial labeling of G if |tdf (i) - tdf (j)| ≤ 1, i, j ∈ {0; 1; 2; ⋯ ; k - 1} where tdf (x) denotes the total number of vertices and the edges labeled with x. A graph with admits a k-total difference cordial labeling is called k-total difference cordial graphs. [ABSTRACT FROM AUTHOR]

Let G be a (p, q) graph and A be a group. Let f : V (G) → A be a function. The order of u ∈ A is the least positive integer n such that un = e. We denote the order of u by o(u). For each edge uv assign the label 1 if (o(f(u)), o(f(v))) = 1 or 0 otherwise. f is called a group A Cordial labeling if |vf (a) − vf (b)| ≤ 1 and |ef (0) − ef (1)| ≤ 1, where vf (x) and ef (n) respectively denote the number of vertices labeled with an element x and number of edges labeled with n(n = 0, 1). A graph which admits a group A Cordial labeling is called a group A Cordial graph. In this paper we define group {1,−1, i,−i} Cordial graphs and prove that the Jahangir graph J3,n(n ≥ 3),the Jelly fish graphs J(m, n)(m ≤ n), the Dumbbell graph Dbn and the Flower graph Fln are all group {1,−1, i,−i} Cordial for every n. [ABSTRACT FROM AUTHOR]

Let G be a (p, q) graph. Let f : V (G) → {1, 2,···, k} be a map where k ∈ N and k > 1. For each edge uv, assign the label gcd(f(u), f(v)). f is called k-total prime cordial labeling of G if |tf (i) - tf (j)| ≤ 1, i, j ∈ {1, 2, · · ·, k} where tf (x) denotes the total number of vertices and the edges labelled with x. A graph with a k-total prime cordial labeling is called k-total prime cordial graph. In this paper we investigate the 4-total prime cordial labeling for some subdivided graphs. [ABSTRACT FROM AUTHOR]