Edge Product Cordial Labeling Research Articles

4-total edge product cordial for some star related graphs

<p>Let G = (V (G), E(G)) be a graph, define an edge labeling function ψ from E(G) to {0, 1, . . . , k − 1} where k is an integer, 2 ≤ k ≤ |E(G)|, induces a vertex labeling function ψ∗ from V (G) to {0, 1, . . . , k − 1} such that ψ∗(v) = ψ(e1) × ψ(e2) × . . . × ψ(en) mod k where e1, e2, . . . , en are all edge incident to v. This function ψ is called a k-total edge product cordial (or simply k-TEPC) labeling of G if the absolute difference between number of vertices and edges labeling with i and number of vertices and edges labeling with j no more than 1 for all i, j ∈ {0, 1, . . . , k − 1}. In this paper, 4-total edge product cordial labeling for some star related graphs are determined.</p>

Total Product and Total Edge Product Cordial Labelings of Dragonfly Graph (Dgn)

In this paper, we study the total product and total edge product cordial labeling for dragonfly graph Dgn. We also define generalized dragonfly graph and find product cordial and total product cordial labeling for this family of graphs.

3-Total Edge Product Cordial Labeling for Stellation of Square Grid Graph

Let G be a simple graph with vertex set V G and edge set E G . An edge labeling δ : E G ⟶ 0,1 , … , p − 1 , where p is an integer, 1 ≤ p ≤ E G , induces a vertex labeling δ ∗ : V H ⟶ 0,1 , … , p − 1 defined by δ ∗ v = δ e 1 δ e 2 ⋅ δ e n mod p , where e 1 , e 2 , … , e n are edges incident to v . The labeling δ is said to be p -total edge product cordial (TEPC) labeling of G if e δ i + v δ ∗ i − e δ j + v δ ∗ j ≤ 1 for every i , j , 0 ≤ i ≤ j ≤ p − 1 , where e δ i and v δ ∗ i are numbers of edges and vertices labeled with integer i , respectively. In this paper, we have proved that the stellation of square grid graph admits a 3-total edge product cordial labeling.

English

In this paper we obtain the total edge product cordial labeling of some corona graphs.

On 3-total edge product cordial labeling of grid

Let us consider a mapping [Formula: see text] of a graph [Formula: see text], where [Formula: see text] is an integer, [Formula: see text]. The mapping [Formula: see text] induces for every vertex [Formula: see text] of [Formula: see text] the label [Formula: see text]. Let [Formula: see text] ([Formula: see text]) denote the number of edges (vertices) in [Formula: see text] that are labeled with the number [Formula: see text] under the labeling [Formula: see text], [Formula: see text].The function [Formula: see text] is called a [Formula: see text]-total edge product cordial labeling of [Formula: see text] if [Formula: see text] for [Formula: see text]. A graph [Formula: see text] with a [Formula: see text]-total edge product cordial labeling is called a [Formula: see text]-total edge product cordial graph.In this paper, we prove that the grid graph [Formula: see text] for [Formula: see text] admits a [Formula: see text]-total edge product cordial labeling.

Matrix Coding Technique on Sunflower Graphs with Edge Product Cordial Labeling

In this paper we develop a technique of coding a secret messages using Sun Flower graphs SFn by subdividing edges and applying edge product cordial labeling. The induced vertex labeling function defined by the product of labels of incident edges to each vertex is such that the number of edges with label 0 and 1 differ by atmost 1. Here, we discuss edge product cordial labeling for sunflower graphs subdivided edges and developed a coding technique of transforming plain text (Text message) in to Cipher Text (Matrix code) and established algorithm. By recent development in coding theory involving programming concepts in any computer languages, this article will revisit without programming method, the matrix coding technique is developed.

On 3-total edge product cordial labeling of tadpole, book and flower graphs

On 3-total edge product cordial labeling of tadpole, book and flower graphs

The total edge product cordial labeling of graph with pendant vertex

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.

On edge product cordial graphs

An edge product cordial labeling is a variant of the well-known cordial labeling. In this paper we characterize graphs admitting an edge product cordial labeling. Using this characterization we investigate the edge product cordiality of broad classes of graphs, namely, dense graphs, dense bipartite graphs, connected regular graphs, unions of some graphs, direct products of some bipartite graphs, joins of some graphs, maximal \(k\)-degenerate and related graphs, product cordial graphs.

On total edge product cordial labeling of fullerenes

For a simple graph G = ( V , E ) this paper deals with the existence of an edge labeling φ : E ( G ) → {0, 1, …, k − 1} , 2 ≤ k ≤ ∣ E ( G )∣ , which induces a vertex labeling φ * : V ( G ) → {0, 1, …, k − 1} in such a way that for each vertex v , assigns the label $\varphi(e_1)\cdot\varphi(e_2)\cdot\ldots\cdot \varphi(e_n) \pmod k$ , where e 1 , e 2 , …, e n are the edges incident to the vertex v . The labeling φ is called a k -total edge product cordial labeling of G if ∣( e φ ( i ) + v φ * ( i )) − ( e φ ( j ) + v φ * ( j ))∣ ≤ 1 for every i , j , $0 \le i l j \le k-1$ , where e φ ( i ) and v φ * ( i ) is the number of edges and vertices with φ ( e ) = i and φ * ( v ) = i , respectively. The paper examines the existence of such labelings for toroidal fullerenes and for Klein-bottle fullerenes.

On 3-total edge product cordial labeling of a carbon nanotube network

For a simple graph G=(V,E) with the vertex set V and the edge set E and for an integer k, 2≤k≤|E(G)|, an edge labeling φ:E(G)→{0,1,…,k−1} induces a vertex labeling φ∗:V(G)→{0,1,…,k−1} defined by φ∗(v)=φ(e1)⋅φ(e2)⋅…⋅φ(en)(modk), where e1,e2,…,en are the edges incident to the vertex v. The function φ is called a k-total edge product cordial labeling of G if |(eφ(i)+vφ∗(i))−(eφ(j)+vφ∗(j))|≤1 for every i,j, 0≤i<j≤k−1, where eφ(i) and vφ∗(i) are the number of edges and vertices with φ(e)=i and φ∗(v)=i, respectively.In this paper, we investigate the 3-total edge product cordial labeling of a carbon nanotube network.

3-total edge product cordial labeling of some new classes of graphs

In this paper we study 3-total edge product cordial (3-TEPC) labeling of some new classes of graphs. We study ladder graph, wheel graph, m isomorphic copies of n–cycle graph and dutch windmill graph in the context of 3-TEPC labeling. We also studied 3-TEPC labeling of some particular examples of graph operations like corona graphs and subdivision graphs.

3-total edge product cordial labeling of rhombic grid

For a simple graph G=(V(G),E(G)), this paper deals with the existence of an edge labeling χ:E(G)→{0,1,…,k−1},2≤k≤|E(G)|, which induces a vertex labeling χ∗:V(G)→{0,1,…,k−1} in such a way that for each vertex v, assigns the label χ(e1)⋅χ(e2)⋅⋯⋅χ(en)((modk)), where e1,e2,…,en are the edges incident to the vertex v. The labeling χ is called a k-total edge product cordial labeling of G if |(eχ(i)+vχ∗(i))−(eχ(j)+vχ∗(j))|≤1 for every i,j,0≤i<j≤k−1, where eχ(i) and vχ∗(i) are the number of edges and vertices with χ(e)=i and χ∗(e)=i, respectively. In this paper, we examine the existence of such labeling for rhombic grid graph.

3-total edge product cordial labeling of wheel related graphs

For a graph G = (V (G), E(G)), an edge labeling function f : E(G) → {0, 1, · · · , k − 1} where k is an integer, 2 ≤ k ≤ |E(G)|, induces a vertex labeling function f*: V (G) → {0, 1, · · · , k − 1} such that f*(v) is the product of the labels of the edges incident to v (mod k). This function f is called k-total edge product cordial (or simply k-TEPC) labeling of G if |(vf (i) + ef (i)) − (vf (j) + ef (j))| ≤ 1 for all i, j ϵ {0, 1, · · · , k−1}. In this paper, 3-total edge product cordial labeling for wheel related graphs is determined.

On [formula omitted]-total edge product cordial labeling of honeycomb

For a graph G=(V(G),E(G)), an edge labeling φ:E(G)→{0,1,…,k−1} where k is an integer, 2≤k≤|E(G)|, induces a vertex labeling φ∗:V(G)→{0,1,…,k−1} defined by φ∗(v)=φ(e1)⋅φ(e2)⋅…⋅φ(en)(modk), where e1,e2,…,en are the edges incident to the vertex v. The function φ is called a k-total edge product cordial labeling of G if |(eφ(i)+vφ∗(i))−(eφ(j)+vφ∗(j))|≤1 for every i,j, 0≤i<j≤k−1, where eφ(i) and vφ∗(i) are the number of edges e and vertices v with φ(e)=i and φ∗(v)=i, respectively.In this paper, we investigate the existence of 3-total edge product cordial labeling of hexagonal grid.

Some new standard graphs labeled by 3–total edge product cordial labeling

AbstractIn this paper, we study 3–total edge product cordial (3–TEPC) labeling which is a variant of edge product cordial labeling. We discuss Web, Helm, Ladder and Gear graphs in this context of 3–TEPC labeling. We also discuss 3–TEPC labeling of some particular examples with corona graph.

On 3-total edge product cordial connected graphs

A \(k\)-total edge product cordial labeling is a variant of the well-known cordial labeling. In this paper we characterize connected graphs of order at least 15 admitting a 3-total edge product cordial labeling.

Edge Product Cordial Labeling of Some Cycle Related Graphs

For a graph having no isolated vertex, a function 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 is such that the number of edges with label 0 and the number of edges with label 1 differ by at most 1 and the number of vertices with label 0 and the number of vertices with label 1 also differ by at most 1. In this paper, we discuss edge product cordial labeling for some cycle related graphs.

Some Edge Product Cordial Graphs in the Context of Duplication of Some Graph Elements

For a graph, a function is called an edge product cordial labeling of G, if the induced vertex labeling function is defined by the product of the labels of the incident edges as such that the number of edges with label 1 and the number of edges with label 0 differ by at most 1 and the number of vertices with label 1 and the number of vertices with label 0 differ by at most 1. In this paper, we show that the graphs obtained by duplication of a vertex, duplication of a vertex by an edge or duplication of an edge by a vertex in a crown graph are edge product cordial. Moreover, we show that the graph obtained by duplication of each of the vertices of degree three by an edge in a gear graph is edge product cordial. We also show that the graph obtained by duplication of each of the pendent vertices by a new vertex in a helm graph is edge product cordial.

Edge product Cordial Labeling and Total Magic Cordial Labeling of Regular Digraphs

Edge product Cordial Labeling and Total Magic Cordial Labeling of Regular Digraphs