A note on difference cordial graphs

2015

In this paper we introduce some results in dierence cordial graphs and the dierence cordial labeling for some families of graphs as: ladder ,triangular ladder,grid,step ladder and two sided step ladder graph. Also we discussed some families of graphs which may be dierence cordial or not,such as diagonal ladder and some types of one-point union graphs.

Journal of Applied Mathematics and Computational Mechanics, 2019

For a graph G = (V (G), E(G)) having no isolated vertex, a function f : E(G) → {0, 1} is called an edge product cordial labeling of graph G, if the induced vertex labeling function defined by the product of labels of incident edges to each vertex be such that the number of edges with label 0 and the number of edges with label 1 differ by at the most 1 and the number of vertices with label 0 and the number of vertices with label 1 also differ by at the most 1. In this paper we discuss the edge product cordial labeling of the graphs W (t) n , PS n and DPS n .

European Journal of Mathematics and Statistics, 2025

Let G be the graph. A topological cordial labeling of a graph G with |V (G)| = n is an injective function f from the vertex set V(G) to the set 2 X where X is a nonempty set such that |X| < n and it forms a topology on X, denoted by {f (V (G))}, that induced a function f * from E (G) → {0, 1} defined by f * (uv) = 1 if f (u) ∩ f (v) is not an empty set and not a singleton set 0 otherwise , for all uv ∈ E (G) such that e f (0)e f (1) ≤ 1 where e f (0) is the number of vertices labeled with 0 and where e f (1) is the number of vertices labeled with 1. The graph that satisfies the condition of a topological cordial labeling is called topological cordial graph.

Annals of Pure and Applied Mathematics, 2020

An injective function ݂ from vertex set ‫)ܩ(ܸ‬ of a graph ‫ܩ‬ to the set ‫ܨ{‬ , ‫ܨ‬ ଵ , ‫ܨ‬ ଶ , ⋯ , ‫ܨ‬ }, where ‫ܨ‬ is the ݅ ୲ Fibonacci number (݅ = 0,1, ⋯ , ݊), is said to be Fibonacci cordial labeling if the induced function ݂ * from the edge set ‫)ܩ(ܧ‬ the set {0,1} defined by ݂ * ‫)ݒݑ(‬ = ‫)ݑ(݂(‬ + ‫݀‪))(m‬ݒ(݂‬ 2) satisfies the condition |݁ (0) − ݁ (1)| ≤ 1, where ݁ (0) is the number of edges with label 0 and ݁ (1) is the number of edges with label 1. A graph that admits Fibonacci cordial labeling is called Fibonacci cordial graph. In this paper we discuss Fibonacci cordial labeling of the families of complete graphs ‫ܭ‬ , paths ܲ , cycles ‫ܥ‬ , and corona product of ‫ܥ‬ and ‫ܭ‬ for ‫‬ = 1,2, and 3.

—A graph G(p,q) is said to have a totally magic cordial (TMC) labeling with constant C if there exists a mapping f : V(G)∪E(G)→{0,1} such that f(a)+f(b)+f({a,b}) = C (mod 2) for all {a,b}∈E(G) provided the condition |f(0)–f(1)|≤1 is hold, where f(0) = v f (0) + e f (0) and f(1) = v f (1) + e f (1) and v f (i), e f (i); i ∈ {0,1} are, respectively, the number of vertices and edges labeled with i. In this paper, we present the totally magic cordial (TMC) labeling of two families of planar graphs, Pl n and Pl m,n , splitting graph of path, cycle and complete bipartite graph and some special corona graphs.

2019

Let G={V,E} be a graph. A mapping f : V(G)→{0,1} is called Binary Vertex Labeling. A Binary Vertex Labeling of a graph G is called a Cordial Labeling if |v_f (0)-v_f (1)|≤1 and |e_f (0)-e_f (1)|≤1. A graph G is Cordial if it admits Cordial Labeling. Here, we prove that Sunlet graph (S_n) and Shell graph C_((n,n-3)) are Cordial and the Splitting graphs of them are also Cordial.

Open Journal of Discrete Mathematics, 2025

In 2012, Ponraj et al . defined a concept of k-product cordial labeling as follows: Let f be a map from V (G) to {0,1,, k −1} where k is an integer, 1 ≤ k ≤ V (G) . For each edge uv assign the label f (u) f (v)(mod k ) . f is called a k-product cordial labeling if ( ) ( ) 1 f f v i − v j ≤ , and ( ) ( ) 1 f f e i − e j ≤ , i, j ∈{0,1,, k −1} , where ( ) f v x and ( ) f e x denote the number of vertices and edges respectively labeled with x ( x = 0,1,, k −1). Motivated by this concept, we further studied and established that several families of graphs admit k-product cordial labeling. In this paper, we show that the path graphs n P admit k-product cordial labeling.

IOP Conference Series: Earth and Environmental Science, 2019

One of the topics in graph theory is labeling. The object of the study is a graph generally represented by vertex, edge and sets of natural numbers called label. For a graph G, the function of vertex labeling g : V (G) → {0, 1} induces an edge labeling function g * : E(G) → {0, 1} defined as g * (uv) = g(u)g(v). The function g is called total product cordial labeling of G if |(vg(0) + eg(0)) − (vg(1) + eg(1))| ≤ 1 with vg(0),vg(1),eg(0),and eg(1) respectively are the number of vertex which has label zero, the number of vertex which has label one, the number of edge which has label zero and the number of edge which has label one. All graphs used in this paper are simple and connected graphs. In this paper, we will prove that some graphs with pendant vertex admit total edge product cordial labeling.

2016

An integer cordial labeling of a graph G(V, E) is an injective map f from V to or as p is even or odd, which induces an edge labeling f * : E → {0, 1} defined by f * (uv) = 1 if f(u) + f(v) ≥ 0 is positive and 0 otherwise such that the number of edges labeled with1and the number of edges labeled with 0 differ atmost by 1. If a graph has integer cordial labeling, then it is called integer cordial graph . In this paper, we introduce the concept of integer cordial labeling and prove that some standard graphs are integer cordial.

International Journal of Innovative Research in Pure and Engineering Mathematics, 2017

Let G be a graph of order p and size q. Let f: V (G) → Z 4 -{0} be a function. (mod 3) where f (u) ≥ f (v). If the number of vertices having label i and the number of vertices having label j differ by maximum 1, the number of edges having label k and the number of edges having label l differ by maximum 1 then the function f is said to be quotient-3 cordial labeling of G. 1 ≤ i, j ≤ 3, i ≠ 𝑗 and 0 ≤ k, l ≤ 2, k ≠ l. Here we proved that some special graphs like Bull, Butterfly, Diamond, Cubical graph Q 3 , Durer, Frucht, Herschel, Moser Spindle, Wagner, Heawood and Truncated tetrahedran graphs are quotient-3 cordial.