Cordial Graph Research Articles

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.

\(4\)-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.

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.

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.

ENERGY OF FIBONACCI PRODUCT CORDIAL GRAPH

Let G be a Fibonacci product cordial graph with n vertices. Then the Fibonacci product cordial label energy of G is denoted by EFPCL [G] and is defined as EFPCL[G]= n i=1 |ρi|, where ρi are the eigenvalues of the Fibonacci product cordial labeled matrix. In this paper, we introduce the Fibonacci product cordial labeled matrix, Fibonacci Product Cordial Labeled Laplacian matrix, Fibonacci product cordial label Laplacian energy, Fibonacci product cordial label equi-laplacian energic graphs respectively.

Some Characterizations and NP-Complete Problems for Power Cordial Graphs

A power cordial labeling of a graph G = V G , E G is a bijection f : V G ⟶ 1,2 , … , V G such that an edge e = u v is assigned the label 1 if f u = f v n or f v = f u n , for some n ∈ N ∪ 0 and the label 0 otherwise, and satisfy the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. The graph that admits power cordial labeling is called a power cordial graph. In this paper, we derive some characterizations of power cordial graphs as well as explore NP-complete problems for power cordial labeling. This work also rules out any possibility of forbidden subgraph characterization for power cordial labeling.

On Fibonacci Cordial Labeling of Some Snake Graphs

Let an injective function f from vertex set V of a graph G to the set (F0, F1, F2, ..., Fn), where Fj is jth the Fibonacci number (j=0, 1, ..., n), is said to be Fibonacci cordial labeling if the induced function f* from the edge set E of graph G to the set {0,1} defined by f* (uv) = (f(u)+f(v)) (mod2) satisfies the condition |ef(0)- ef(1) ≤ 1, where ef(0) is the number of edges with label 0 and ef(1) is the number of edges with label 1. A graph which admits Fibonacci cordial labeling is called Fibonacci cordial graph.

Union Of 4-Total Prime Cordial Graph G With The Bistar Bn,N

Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map where k ∈ N is a variable and k > 1. For each edge uv, assign the label gcd(f (u), f (v)). The map f is called a k- Total prime cordial labeling of G if |tpf (i) − tpf (j)| ≤ 1, i, j ∈
 {1, 2, · · · , k} where tpf (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 of G ∪ Bn,n, where G has a 4-total prime cordial labeling and Bn,n is a bistar.

Additive Inverse Cordial Labeling of Graphs

Let be a graph. Consider the function from to the set and the induced surjective edge function defined by . Let and respectively denote the number of vertices labelled by x, where , and number of edges labelled by , where . Then Ψ is said to be an additive inverse cordial labelingif , where and . If G has an additive inverse cordial labeling Ψ then we say that G is an additive inverse cordial graph.

K-Product cordial labeling of product of graphs

In 2012, Ponraj et al. defined k-product cordial labeling as follows: Let [Formula: see text] be a map from [Formula: see text] to [Formula: see text] where [Formula: see text] is an integer, [Formula: see text]. For each edge [Formula: see text] assign the label [Formula: see text] [Formula: see text]. [Formula: see text] is called a k-product cordial labeling if [Formula: see text], and [Formula: see text], [Formula: see text], where [Formula: see text] and [Formula: see text] denote the number of vertices and edges, respectively, labeled with [Formula: see text] [Formula: see text]. A graph that admits k-product cordial labeling is called k-product cordial graph. Later, we proved that several families of graphs are k-product cordial graphs. In this paper, we show that the product of graphs admit k-product cordial labeling.

Product Cordial Labelling for Some Bicyclic Graphs

A graph \(G\) with lines and points is known as a product cordial graph if there occurs a labeling \(g\) from \(V(G)\) to \(\{0,1\}\) such that if every line \(rt\) is given the labeled \(g(r) .g(t)\), then the cardinality of points with labeled zero and the cardinality of points with labeled one vary as a maximum by one and the cardinality of lines with labeled zero and the cardinality of lines with labeled one vary by as a maximum one. In this case, \(g\) is alleged the product cordial labeling of \(G\). This paper deals with product cordial labeling for some graphs related to bicyclic graph such as \(B[n,n]\), \(B[n,n]*S_m\), \(B[n,n]*P_2*S_m\) and \(B[n,n]*P_3*S_m\), \(B[n,n] \odot K_2\), \(B[n,n] \odot K_3\).

Group S4 Difference Cordial Labeling

Objective: To find the Group S4 difference cordial labeling of some standard graphs. Method: Path, Cycle and some standard graphs are converted into Group S4 difference cordial graphs by labeling the vertices with the elements of S4 and the edges as the difference of the order of the elements labeled to the vertices of the graph. Findings: Group S4 difference cordial labeling for path, cycle and some standard graphs. Novelty: Graph labeling can use for issues in Mobile Adhoc Networks such as connectivity, scalability, routing, modeling the network and simulation. In this paper we compute the new concept of Group S4 difference cordial labeling and also we prove that some standard graphs are Group S4 difference cordial graph. AMS Subject Classification 2010: 05C78 Keywords: Difference cordial Labeling; Path; cycle; Bistar; Comb; Ladder; S4

Double Divisor Cordial Labeling of Graphs

In this paper a new variant of divisor cordial labeling (DCL) named double divisor cordial labeling (DDCL) is in-troduced. A DDCL of a graph Gω having a node set Vω is a bijection gω from Vω to {1,2,3,…, |Vω |} such that each edge yz is given the label 1 if 2gω (y)/gω (z) or 2gω (z)/gω (y) and 0 otherwise, then the modulus of difference of edges labeled 0 and those labeled 1 do not exceed 1 i.e; |eg ω (0) — eg ω (1)| ≤ 1. If a graph permits a DDCL, then it is known as double divisor cordial graph (DDCG). In this paper we derive certain general results concerning DDCL and establish the same for some well known graphs.

Prime Cordial Labeling of Generalized Petersen Graph under Some Graph Operations

A graph is a connection of objects. These objects are often known as vertices or nodes and the connection or relation in these nodes are called arcs or edges. There are certain rules to allocate values to these vertices and edges. This allocation of values to vertices or edges is called graph labeling. Labeling is prime cordial if vertices have allocated values from 1 to the order of graph and edges have allocated values 0 or 1 on a certain pattern. That is, an edge has an allocated value of 0 if the incident vertices have a greatest common divisor (gcd) greater than 1. An edge has an allocated value of 1 if the incident vertices have a greatest common divisor equal to 1. The number of edges labeled with 0 or 1 are equal in numbers or, at most, have a difference of 1. In this paper, our aim is to investigate the prime cordial labeling of rotationally symmetric graphs obtained from a generalized Petersen graph P(n,k) under duplication operation, and we have proved that the resulting symmetric graphs are prime cordial. Moreover, we have also proved that when we glow a Petersen graph with some path graphs, then again, the resulting graph is a prime cordial graph.

Union of 3-Total Difference Cordial Graph with the Bistar Bn,n

Union of 3-Total Difference Cordial Graph with the Bistar Bn,n

Sum divisor cordial labeling in the context of graph operations on grötzsch

A Sum divisor cordial labeling of a graph G with vertex set V is a bijection r from V to {1,2,3,...,|V (G )|} such that an edge uv is assigned the label 1 if 2 divides r(u)+ r (v ) and 0 otherwise; and the number of edges labeled with 0 and the number of edges labeled with 1differ by at most 1 . A graph with a sum divisor cordial labeling is called sum divisor cordial graph. In this research paper, we investigate the sum divisor cordial labeling bahevior for Grötzsch graph, fusion of any two vertices in Grötzsch graph, duplication of an arbitrary vertex in Grötzsch graph, duplication of an arbitrary vertex by an edge in Grötzsch graph, switching of an arbitrary vertex of degree four in Grötzsch graph, switching of an arbitrary vertex of degree three in Grötzsch graph and path union of two copies of Grötzsch.

Product cordial graph in the context of some graph operations on crown, helm, and wheel graph

Product cordial graph in the context of some graph operations on crown, helm, and wheel graph