• Journal of applied mathematics & informatics
• /
• 제39권1_2호
• /
• pp.223-237
• /
• 2021

Let G = (V (G), E(G)) be a graph and let g : V (G) → S3 be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S3 cordial remainder labeling of G if |vg(i)-vg(j)| ≤ 1 and |eg(1)-eg(0)| ≤ 1, where vg(j) denotes the number of vertices labeled with j and eg(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S3 cordial remainder labeling is called a group S3 cordial remainder graph. In this paper, we prove that square of the path, duplication of a vertex by a new edge in path and cycle graphs, duplication of an edge by a new vertex in path and cycle graphs and total graph of cycle and path graphs admit a group S3 cordial remainder labeling.

• Journal of Applied and Pure Mathematics
• /
• 제4권3_4호
• /
• pp.85-97
• /
• 2022

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}\;=\;\{\array{{\frac{p}{2}}&p\text{ is even}\\{\frac{p-1}{2}}\;&p\text{ is odd,}}$$ and M = {±1, ±2, ⋯ ± 𝜌} called the set of labels. Consider a mapping λ : V → M 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 $\frac{{\lambda}(u)+{\lambda}(v)}{2}$ if λ(u) + λ(v) is even and $\frac{{\lambda}(u)+{\lambda}(v)+1}{2}$ if λ(u) + λ(v) is odd such that ${\mid}\bar{\mathbb{S}}_{{\lambda}_1}-\bar{\mathbb{S}}_{{\lambda}^c_1}{\mid}{\leq}1$ where $\bar{\mathbb{S}}_{{\lambda}_1}$ and $\bar{\mathbb{S}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling of graphs which are obtained from path and cycle.

• Journal of Applied and Pure Mathematics
• /
• 제5권1_2호
• /
• pp.41-53
• /
• 2023

Let G = (V, E) be a (p, q) graph. Define $${\rho}=\{{\frac{2}{p}},\;{\text{{\qquad} if p is even}}\\{\frac{2}{p-1}},\;{{\text{if p is odd}}$$ 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 ${\mid}{\Delta}_{f_1}-{\Delta}_{f^c_1}{\mid}{\leq}1$, where ${\Delta}_{f_1}$ and ${\Delta}_{f^c_1}$ 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 pair difference cordial labeling behaviour of Petersen graphs P(n, k) like P(n, 2), P(n, 3), P(n, 4).

• Journal of Applied and Pure Mathematics
• /
• 제5권3_4호
• /
• pp.237-253
• /
• 2023

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} & \;\;p\text{ is even} \\ {\frac{p-1}{2}} & \;\;p\text{ is odd,}$$ and M = {±1, ±2, … ± ρ} called the set of labels. Consider a mapping λ : V → M 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 ${\frac{{\lambda}(u)+{\lambda}(v)}{2}}$ if λ(u) + λ(v) is even and ${\frac{{\lambda}(u)+{\lambda}(v)+1}{2}}$ if λ(u) + λ(v) is odd such that ${\mid}{\bar{{\mathbb{S}}}}_{\lambda}{_1}-{\bar{{\mathbb{S}}}}_{{\lambda}^c_1}{\mid}{\leq}1$ where ${\bar{{\mathbb{S}}}}_{\lambda}{_1}$ and ${\bar{{\mathbb{S}}}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of few graphs including the closed helm graph, web graph, jewel graph, sunflower graph, flower graph, tadpole graph, dumbbell graph, umbrella graph, butterfly graph, jelly fish, triangular book graph, quadrilateral book graph.

• Journal of applied mathematics & informatics
• /
• 제32권3_4호
• /
• pp.377-387
• /
• 2014

Let G be a (p, q) graph. Let f be a map from V (G) to {1, 2, ${\ldots}$, p}. For each edge uv, assign the label ${\mid}f(u)-f(\nu){\mid}$. f is called a difference cordial labeling if f is a one to one map and ${\mid}e_f(0)-e_f(1){\mid}{\leq}1$ where $e_f(1)$ and $e_f(0)$ denote the number of edges labeled with 1 and not labeled with 1 respectively. A graph with admits a difference cordial labeling is called a difference cordial graph. In this paper, we investigate the difference cordial labeling behavior of triangular snake, Quadrilateral snake, double triangular snake, double quadrilateral snake and alternate snakes.

• Journal of applied mathematics & informatics
• /
• 제42권1호
• /
• pp.1-14
• /
• 2024

Let G = (V, E) be a (p, q) graph. Define $$\begin{cases}\frac{p}{2},\:if\:p\:is\:even\\\frac{p-1}{2},\:if\:p\:is\:odd\end{cases}$$ 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 |Δ_f1 - Δ_f^c1| ≤ 1, where Δ_f1 and Δ_f^c1 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 subdivision of some graphs.

• Journal of Applied and Pure Mathematics
• /
• 제4권5_6호
• /
• pp.317-329
• /
• 2022

In this paper we investigate the pair difference cordial labeling behaviour of m- copies of K₄, subdivision of star, fan, comb graphs.

• Journal of Applied and Pure Mathematics
• /
• 제5권5_6호
• /
• pp.363-373
• /
• 2023

In this paper we investigate the 4-total mean cordial labeling behavior of arrow graphs, shell-Butterfly graph and graphs obtained by joining two copies of shell graphs by a path.

• Journal of applied mathematics & informatics
• /
• 제39권3_4호
• /
• pp.497-506
• /
• 2021

Let G be a graph. Let f : V (G) → {0, 1, …, k - 1} be a function where k ∈ ℕ and k > 1. For each edge uv, assign the label $f(uv)={\lceil}{\frac{f(u)+f(v)}{2}}{\rceil}$. f is called k-total mean cordial labeling of G if ${\mid}t_{mf}(i)-t_{mf}(j){\mid}{\leq}1$, for all i, j ∈ {0, 1, …, k - 1}, where t_mf (x) denotes the total number of vertices and edges labelled with x, x ∈ {0, 1, …, k-1}. A graph with admit a k-total mean cordial labeling is called k-total mean cordial graph.