Cordial Labeling Research Articles

Binary vertex labelings of graphs and digraphs

A (0; 1)-labeling of a set is said to be friendly if the number of elements of the set labeled 0 and the number labeled 1 differ by at most 1. Let g be a labeling of the edge set of a graph that is induced by a labeling f of the vertex set. If both g and f are friendly then f is said to be a cordial labeling of the graph. This concept extended to directed graphs is called (2; 3)-cordiality of digraphs. We investigate the labelings that are both cordial for a graph and (2; 3)-cordial for an orientation of it. We also consider the same problem for other known binary vertex labelings of graphs.

GROUP MEAN CORDIAL LABELING OF SOME QUADRILATERAL SNAKE GRAPHS

Let G be a (p, q) graph and let A be a group. Let f : V (G) −→ A be a map. For each edge uv assign the label [o(f (u))+o(f (v)) / 2]. Here o(f (u)) denotes the order of f (u) as an element of the group A. Let I be the set of all integerslabeled by the edges of G. f is called a group mean cordial labeling if the following conditions hold: (1) For x, y ∈ A, |vf (x) − vf (y)| ≤ 1, where vf (x) is the number of vertices labeled with x. (2) For i, j ∈ I, |ef (i) − ef (j)| ≤ 1, where ef (i) denote the number of edges labeled with i. A graph with a group mean cordial labeling is called a group mean cordial graph. In this paper, we take A as the group of fourth roots of unity and prove that, Quadrilateral Snake, Double Quadrilateral Snake, Alternate Quadrilateral Snake and Alternate Double Quadrilateral Snake are groupmean cordial graphs.

Pair mean cordial labeling of udukkai, octopus, drum and fire cracker graphs

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.

On Cordial Labeling of Third Power of Path with Other Graphs

On Cordial Labeling of Third Power of Path with Other Graphs

Exploring Mean Cordial Labeling Possible Combination Position of Vertices in Graphs: A Computational Approach

Objectives: We have developed the Python module of mean cordial labeling for the different types of graphs, like Path, Cycle, and Subdivision of Star graphs. We aim to identify the number of combination positions of vertices that satisfy the mean cordial labeling rules. We have found mathematical equations that describe the labeling behavior in these graphs. Methods: In this paper, a Python program was developed to find the mean cordial labeling of the Path, Cycle, and Subdivision of the Star graph. We have obtained the number of combination positions of vertex obeying the mean cordial labeling condition using this Python module. We have drawn the graph between the number of vertices and the number of combination positions of the vertex. Findings: We have found that the different graph types like Path, Cycle, and Subdivision of Star graph satisfy the mean cordial labeling condition. The result indicates that the number of combination positions of the Path and cycle graph fulfill the power equation Y=a*xb and the Subdivision of the Star graph meets the exponential growth equation Y=a*bx. Novelty: In this paper, a new method has been developed to find the number of combination position of varies graphs using the Python module. This computational approach will be useful to analyze the biological networking and protein-protein interaction study. Keywords: Mean Cordial, Path, Cycle, Subdivision of Star graph, Computational graph theory

PAIR MEAN CORDIAL LABELING OF HURDLE, KEY, LOTUS, AND NECKLACE GRAPHS

Let be a graph with vertices and edges. Define and . Consider a mapping by assigning different labels in to the different elements of when is even and different labels in to elements of V and repeating a label for the remaining one vertex when is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge of G, there exists a labeling if is even and if is odd such that | |≤1 where and respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there is a pair mean cordial labeling is called pair mean cordial graph(PMC-graph). In this paper, we investigate the pair mean cordial labeling of some graphs like hurdle graph, lotus graph, necklace graph, F-tree, Y-tree, subdivided shell graph, uniform bow graph and key graph.

RETRACTED: ELrokh et al. On Cubic Roots Cordial Labeling for Some Graphs. Symmetry 2023, 15, 990

The journal Symmetry retracts the article titled “On Cubic Roots Cordial Labeling for Some Graphs” [...]

A Family of Join Spider Graphs on Sum Divisor Cordial Labeling with Application

A graph G with p vertices and q edges is said to be a Sum Divisor Cordial labelling. If ????: ???? → 1,2, … ???? such that for each edge ???????????????? assign the label 1, if 2|(???? ???? + ????(????)| and 0 otherwise, satisfying the condition |e????(1)- e???? 0 | ≤ 1, where e????(1) is the number of edges labelled with 1 and e????(0) is the number of edges labelled with 0. A graph with a sum divisor cordial labeling graph. In this paper we study and we prove that for a class of Join Spider graphs with atmost one additional leg namely JSP(1m,2n), JSP(1m,2n,32), JSP(1m,2n,42), JSP(1m,2n,52). In this paper we identify an application using Affline Cipher for Cyber Security through encryption and decryption.

Mean Cordial Labeling in Graph Representations of Human Anatomy and Circulatory Systems

Mean Cordial Labeling in Graph Representations of Human Anatomy and Circulatory Systems

Cordial Digraphs

A ( 0 , 1 ) -labeling of a set is said to be friendly if the number of elements of the set labeled 0 and the number labeled 1 differ by at most 1. Let g be a labeling of the edge set of a graph that is induced by a labeling f of the vertex set. If both g and f are friendly then g is said to be a cordial labeling of the graph. We extend this concept to directed graphs and investigate the cordiality of directed graphs. We show that all directed paths and all directed cycles are cordial. We also discuss the cordiality of oriented trees and other digraphs.

\(4\)-Total Prime Cordial Labeling of Some Derived Graphs

Let \(G\) be a \((p, q)\) graph. Let \(f: V(G) \to \{1, 2, \ldots, k\}\) be a map where \(k \in \mathbb{N}\) is a variable 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 \(\left|t_{f}(i) – t_{f}(j)\right| \leq 1\), \(i, j \in \{1, 2, \ldots, k\}\) where \(t_{f}(x)\) denotes the total number of vertices and edges labeled 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 of some graphs like dragon, Möbius ladder, and corona of some graphs.

Some results on root cube mean cordial labeling

All the graphs considered in this paper are simple and undirected. Let [Formula: see text] be a simple undirected graph. A function [Formula: see text] is called root cube mean cordial labeling if the induced function [Formula: see text] defined by [Formula: see text] satisfies the condition [Formula: see text] and [Formula: see text] for any [Formula: see text], where [Formula: see text] and [Formula: see text] denotes the number of vertices and number of edges with label [Formula: see text], respectively, and [Formula: see text] denotes the greatest integer less than or equals to [Formula: see text]. The [Formula: see text] is called root cube mean cordial if it admits root cube mean cordial labeling. In this paper, we have discussed root cube mean cordial labeling of some graphs. Also, we have provided some graphs which are not root cube mean cordial.

On bijective product square k-cordial labeling

A bijective product square [Formula: see text]-cordial labeling of a graph [Formula: see text] with vertex set [Formula: see text] and edge set [Formula: see text] is a bijection [Formula: see text] from [Formula: see text] to [Formula: see text] such that the induced edge function [Formula: see text] from [Formula: see text] to [Formula: see text] defined as [Formula: see text] for every edge [Formula: see text] satisfies the following condition. (i) If [Formula: see text] is the number of edges labeled with [Formula: see text] under [Formula: see text], then [Formula: see text] where [Formula: see text]. A graph which admits a bijective product square [Formula: see text]-cordial labeling is called bijective product square [Formula: see text]-cordial graph. In this paper, we find upper limit of the size of the bijective product square [Formula: see text]-cordial graph for [Formula: see text] and [Formula: see text]. Also, we prove that every graph is a subgraph of a connected bijective product square [Formula: see text]-cordial graph for all odd prime [Formula: see text]. In addition, we establish the relation between bijective product square [Formula: see text]-cordial and [Formula: see text]-product cordial graphs.

A single assignment of numbers for square divisor cordial and cube divisor cordial labelings on the generalized Petersen graphs GP (n,3)

In this paper, a work on the generalized Petersen graph GP [Formula: see text] is done, proving Generalized Petersen graph GP [Formula: see text] to be both Square Divisor Cordial Graphs and Cube Divisor Cordial Graphs by a single assignment of numbers on the same graph. Few conditions are provided to label the graphs in single assignment to prove two different labelings. A rule is developed to label the graphs and the results obtained are tabulated by actual verification for [Formula: see text] to [Formula: see text] but the rule holds good for all [Formula: see text] 4. Further, a few illustrations are provided to justify the rule given to label the graphs in a single assignment.

Harmonic Mean Cordial Labeling of Some Cycle Related Graphs

Harmonic Mean Cordial Labeling of Some Cycle Related Graphs

Sum Divisor Cordial Labeling of T p -Tree Related Graphs

A sum divisor cordial labeling of a graph G with vertex set V ( G ) is a bijection f from V ( G ) to { 1 , 2 , ⋯ , | V ( G ) | } such that an edge u v is assigned the label 1 if 2 divides f ( u ) + f ( v ) and 0 otherwise; and the number of edges labeled with 1 and the number of edges labeled with 0 differ by at most 1 . A graph with a sum divisor cordial labeling is called a sum divisor cordial graph. In this paper, we discuss the sum divisor cordial labeling of transformed tree related graphs.

Harmonic Mean Cordial Labeling of One Chord Cn V G

All the graphs considered in this article are simple and undirected. Let G = (V (G),E(G)) be a simple undirected graph. A function is called Harmonic Mean Cordial if the induced function defined by satisfies the condition and for any , where and denote the number of vertices and number of edges with label respectively and denotes the greatest integer less than or equals to . A graph is called a harmonic mean cordial graph if it admits harmonic mean cordial labeling. In this article, we have discussed the harmonic mean cordial labeling of One Chord .

A Study on Sum Divisor Cordial Labeling Graphs

Cordial labeling refers to a graph with vertices and edges as a sum divisor if there exists a bijection function such that for each edge assign the label 1 , if and 0 otherwise, satisfying the condition is the number of edges having the label 1 , and is the number of edges having the label 0 . A graph with sum-divisor cordial labeling is called a sum-divisor cordial graph. In the paper, we establish this alternate triangular belt graph, twig graph, duplication of the top vertex Alternate triangular snake graph, duplication of top vertex Pentagon snake graph, jellyfish when and are even, Spider graph with n spokes .

Group Difference Cordial Labeling in Graphs

. Let group .For
 denotes 
 . 
 which is the group of fourth roots of unity, that is cyclic with generators i and -i. We proved that path graph, bistar graph, and Crown graph are We Ladder graph, and star graph is a difference cordial graph.

Cordial Labeling of Corona Product between Paths and Fourth Power of Paths

Cordial Labeling of Corona Product between Paths and Fourth Power of Paths