Cordial Labeling Research Articles

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.

Prime cordial labeling of n-chain vertex merged staircase graphs

A prime cordial labeling of a graph G with vertex set V is a bijection h:V → {1,2,..|V|} such that, for each edgeuv, the label 1 is assigned, if g.c.d[h(u), h(y)] = 1, otherwise 0, and the total number of edges labeled as 0, and the total number of edges labeled as 1, differ atmost by 1. In this paper, we prove that n-chain vertex merged staircase graphs are prime cordial.

3-Vertex Friendly Index Set of Graphs

Graph labeling is an assignment of integers to the vertices or the edges, or both, subject to certain conditions. In literature we find several labelings such as graceful, harmonious, binary, friendly, cordial, ternary and many more. A friendly labeling is a binary mapping such that where and represents number of vertices labeled by 1 and 0 respectively. For each edge assign the label , then the function f is cordial labeling of G if and , where and are the number of edges labeled 1 and 0 respectively. A friendly index set of a graph is { runs over all f riendly labeling f of G} and it is denoted by FI(G). A mapping is called ternary vertex labeling and represents the vertex label for . In this article, we extend the concept of ternary vertex labeling to 3-vertex friendly labeling and define 3-vertex friendly index set of graphs. The set runs over all 3 ? vertex f riendly labeling f f or all is referred as 3-vertex friendly index set. In order to achieve , number of vertices are partitioned into such that for all with and la- bel the edge by where . In this paper, we study the 3-vertex friendly index sets of some standard graphs such as complete graph Kn, path Pn, wheel graph Wn, complete bipartite graph Km,n and cycle with parallel chords PCn.

On cordial related labeling of isomorphic copies of paths and subdivision of star

In this paper, we investigate the cordiality of the isomorphic copies of paths mPn . We also give sufficient condition for mPn to admit the prime cordial labeling, product cordial labeling and total product cordial labeling. Furthermore, we also determine the prime cordial labeling, product cordial labeling and total product cordial labeling for subdivision of star under certain conditions.

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.

Further results on Parity Combination Cordial Labeling

Let G be a (p, q)-graph. Let f be an injective mapping from V(G) to {1, 2, …, p}. For each edge xy, assign the label left(genfrac{}{}{0pt}{}{x}{y}right) or left(genfrac{}{}{0pt}{}{y}{x}right) according as x > y or y > x. Call f a parity combination cordial labeling if |ef(0) − ef(1)| ≤ 1, where ef(0) and ef(1) denote the number of edges labeled with an even number and an odd number, respectively. In this paper we make a survey on all graphs of order at most six and find out whether they satisfy a parity combination cordial labeling or not and get an upper bound for the number of edges q of any graph to satisfy this condition and describe the parity combination cordial labeling for two families of graphs.

Divisor cordial labeling in the Context of Friendship Graph

Divisor cordial labeling in the Context of Friendship Graph

A comprehensive survey on prime cordial and divisor cordial labeling of graphs

This article presents a short and concise survey on prime cordial and divisor cordial labeling of graphs. A prime cordial labeling of a graph G(V,E) is a bijective function f:V(G) → {1,2,…,|V|} such that if each edge xy is assigned the label 1 if gcd(f(x),f(y)) = 1 and 0 if gcd(f(x),f(y)) > 1, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. Further, a divisor cordial labeling of G is a bijection g: V(G) → {1,2,…,|V|} such that an edge st is assigned the label 1 if one g(s) or g(t) divides the other and 0 otherwise, then the number of edges labeled with 0 and the number of edges labelled with 1 differ by at most 1. We call G a divisor cordial graph if it admits a divisor cordial labeling. This article stands divided into five sections. The first and fifth sections are reserved respectively for introduction and some important references. The second section deals with the prime cordial labeling of certain classes of graphs wherein some important known results have been recalled. The third section deals with the divisor cordial labeling of graphs in which a few known results of high interest have been outlined. In the fourth section we highlight certain conjectures and open problems in respect of the above mentioned labelling that still remain unsolved.

Fibonacci Cordial Labeling of Some Special Families of Graphs

Fibonacci Cordial Labeling of Some Special Families of Graphs

Investigation on Parity Combination Cordial Labeling of Graphs obtained by Duplication of a vertex by an edge

Investigation on Parity Combination Cordial Labeling of Graphs obtained by Duplication of a vertex by an edge

Integer Cordial Labeling of Some Different Snake Graph

Integer Cordial Labeling of Some Different Snake Graph

SD-Prime Cordial Labeling of K4 −Snake and Related Graphs

SD-Prime Cordial Labeling of K4 −Snake and Related Graphs

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

New Family of Parity Combination Cordial Labeling of Graph

Let G be a (p, q) graph. Let f be an injective map from V(G) to {1, 2, …, p}. For each edge xy, assign the label         y x or         x y according as x > y or y > x. f is called a parity combination cordial labeling (PCC-labeling) if f is a one to one map and | ef(0) − ef(1) |  1 where ef(0) and ef(1) denote the number of edges labeled with an even number and odd number respectively. A graph with a parity combination cordial labeling is called a parity combination cordial graph (PCC-graph). In this paper we investigate the PCC- labeling of the graph G , It is obtained by identifying a vertex vk in G and a vertex of degree n in Hn, where G is a PCC graph with p vertices and q edges under f with f(vk) = 1.

Narayana Prime Cordial Labeling of Cycle Related and Tree Related Graphs

The Narayana prime cordial labeling of a graph GU,E is a process of assigning the binary numbers 0 and 1 to the edges satisfying the cordiality condition through a 11 function on U and an induced function on E. In this manuscript, we compute this labeling to certain cycle related graphs and tree related graphs viz. (i) ladder graph, (ii) wheel graph, (iii) fan graph, (iv) double star graph, (v) bistar graph and (vi) generalized star graph..

PRODUCT CORDIAL LABELING OF DOUBLE PATH UNION OF C3 RELATED GRAPHS

In this paper we discuss The double path unions obtained on C3 related graphs for product cordial labeling given by Pm(2G’) where G’ = C3, FL(C3), C3+, bull, tail(C3,2P2) etc.

Divisor cordial labeling for some cycle and wheel related graphs

Divisor cordial labeling for some cycle and wheel related graphs

Coding Technique with Web Graph and Difference Cordial Labeling

Coding Technique with Web Graph and Difference Cordial Labeling

Some results on E cordial labeling of hypercube related graphs

Some results on E cordial labeling of hypercube related graphs

Several result on SD-prime cordial graphs

A bijection f: V(G) → {1,2,··· ,|V(G)|} induces an edge labeling f∗: E(G) → {0,1} such that for any edge uv in G, f∗(uv) = 1 if gcd(S,D) = 1 and f∗(uv) = 0 otherwise, where S = f(u)+ f(v) and D = |f(u)− f(v)|. The labeling f is called SD-prime cordial labeling if |ef∗(0) − ef∗(1)|≤1. We say that G is SD-prime cordial graph if it admits SD-prime cordial labeling. In this paper, we prove that certain classes of zero-divisor graphs of commutative rings are SD-prime cordial graphs.