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 investigate that cycle with one chord path cycle with one chord, cycle with twin chord path cycle with twin chord admit sum divisor cordial labeling. Kala, difference cordial labeling of graphs, global journal of mathematical sciences. Umbrella graph, p nqs n graph, c nq sn graphs are square difference graphs.
Kragujevacjournalofmathematics volume4022016,pages290297. Z, in other words it is a labeling of all edges by integers. Introduction all graphs considered are finite, simple and undirected. Vertex prime labeling,lcordial labeling,path,cycle. Sathish narayanan, further results on difference cordial labeling of corona graphs, the journal of the indian academy of mathematics, 3520. Vg 0, 1 induces an edge labeling function f e g 0 1, defined as fuvfufv then the function f is said to be total vertex product cordial labeling of g if. In this paper we proved that the umbrella graph um, n, duplication of a vertex by an edge in a cycle cn, duplication of an edge by a vertex in a cycle cn and the total graph of a path pn are difference cordial graphs. On edge product cordial labeling of some product related. Some edge product cordial graphs in the context of. In this paper we prove that the split graphs of k1,n and bn,n are prime cordial graphs. Edge product cordial labeling of some graphs journal of applied.
A graph with a difference cordial labeling is called a difference cordial graph. Quotient 3 cordial labeling for star related graphs. Prime and prime cordial labeling for some special graphs. We prove that the friendship graph, cycle with one chord except when n is even and the chord joining the vertices at diameter distance, cycle with twin chords except when n is even and one of the chord joining the vertices at diameter distance are product cordial graphs. Applications of graph labeling in communication networks. In this paper we investigate product cordial labeling for some new graphs.
Here we prove that the graphs like flower fln, bistar bn,n, square graph of bn,n, shadow graph of. It has a mouse based graphical user interface, works online without installation, and a series of graph properties and parameters can be displayed also during the construction. Graph labeling, cordial labeling, product cordial labeling, kite graph. We prove that the friendship graph, cycle with one chord except when n is even and the chord joining the vertices at diameter distance. The concept of cordial labeling was introduced by cahit 1 in which he proved that the wheel w.
Graph theory has a good development in the graph labeling and has a broad range of applications. This paper provides insights into some aspects of the possibilities and role of mind, consciousness, and their relation to mathematical logic with the application of problem solving in the fields of psychology and graph theory. Definition 1 a graph labeling is an assignment of integers to the vertices or edges. This work also rules out any possibility of forbidden subgraph characterizations for total edge product cordial labeling as it is established that for n2, k n is total edge product cordial graph. Prime cordial labeling of some wheel related graphs. We have investigated 3total edge sum cordial labeling of graphs to. A prime cordial labeling of a graph g with the vertex set v g is a bijection f. For graph theoretic terminology, we refer to harary 2. Cordial labeling is one of the most interesting graph labeling.
Corollary if g is 3 edge sum cordial graph then it is 3total edge sum cordial labeling of graph. They also provide a graphtheoretic realization of the function. One of the important areas in graph theory is graph labeling used in many applications like coding theory, xray crystallography, radar, astronomy, circuit design, communication network addressing, data base management. We investigate mean cordial labeling behavior of paths, cycles, stars, complete graphs, combs and some more standard graphs. A graph with such a labeling is an edge labeled graph. In this paper an analysis is made on union of graphs are prime cordial labeling. Most graph labeling methods trace their origin to one introduced by rosa 8 in 1967, or one given by graham and sloane 4 in 1980. In this paper, i inspect the existence of fibonacci cordial labeling of dspn,dsdfn,edgeduplicationink 1, n,jointsum ofgln,dfn. Graph labeling connects many branches of mathematics and is considered one of important blocks of graph theory, for more details see 3. Introduction the eld of graph theory plays a vital role in various elds. If g is a graph, then a vertex labeling function f.
Pdf cordial labeling for the splitting graph of some standard. A graph g is said to be quotient3 cordial graph if it receives quotient3 cordial labeling. We introduce a new type of graph labeling called as lcordial labeling and show that k 1,n,path p n, c n, sc 3,m are families of lcordial graphs. Graph theory plays an important role for automatic graph generation in computer science technology applications such as database design, software engineering. A graph labeling is an assignment of labels to edges, vertices or both. A graph gis said to be cordial if it admits a cordial labeling. Introduction the concept of graph labeling was introduced by rosa in 1967 6. A prime cordial labeling of a graph with the vertex set is a bijection such that each edge is assigned the label 1 if and 0 if. A binary vertex labeling f of a graph g is called a cordial labeling if jv f1 v f0j 1 and je f1 e f0j 1. The field of graph theory plays an important role in various areas of pure. Cordial labeling for the splitting graph of some standard graphs 107 2 main results theorem 2. Shobana the following graphs are proved as prime cordial labeling. A graph is called cordial if it is possible to label its vertices with 0s and 1s so.
A free graph theory software tool to construct, analyse, and visualise graphs for science and teaching. Graph labeling is a very powerful tool that eventually makes. Note that interchanging the vertex labels 0 and 1 in a cordial labeling results in a new cordial labeling of. The following graphs are proved as prime cordial labeling. Square difference labeling, square difference graph. G maxfdv j v 2 vg is the maximum degree of the vertices in the graph g. A graph which admits prime cordial labeling is called prime cordial graph.
The resulting tree t has n 2 vertices, and so by induction hypothesis it admits a cordial labeling, say f. We also show that the square graph of bn,n is a prime cordial graph while middle graph of pn is a prime cordial graph for n. C4 s w2 and its cordial labeling shown in figure 3. Rosa, on certain valuations of the vertices of a graph, theory of. Graph theory software to at least draw graph based on the program. Signed product cordial labeling in duplicate graphs of. T where each s i is a set of vertices having at least two vertices. Cordial labeling for the splitting graph of some standard. A graph having fibonacci cordial labeling is called fibonacci cordialgraph.
The concept of cordial labeling was introduced by cahit 1. Introduction all graphs in this paper are simple finite undirected and nontrivial graph gv, e with vertex set v and the edge set e. A cordial labeling is a friendly labeling f for which c f. We follow the basic notation and terminology of graph theory as in 7, while for number theory we refer to burton 6 and of graph labeling as in 3. A sum divisor cordial labeling of a graph g with vertex set v is a bijection f from.
Let ct n denote the onepoint union of tcycles of length n. Cordial and product cordial labeling for the extended. Pdf some more sum divisor cordial labeling of graphs. A graph g is product cordial if it admits product cordial labeling. Prime and prime cordial labeling for some special graphs 1. A prime cordial labeling of a graph g with vertex set v is a bijection f from v to 1,2. The concept of cordial graphs was introduced by cahit3.
Cordial labelings were introduced by cahit 1987 as a weakened version of graceful and harmonious. Labeling constructions using digraph products sciencedirect. A binary vertex labeling of a graph g is called a cordial labeling if. Keywords graph labeling, duplicate graph, triangular ladder, bistar, double star, signed product cordial labeling. For the remainer of this paper whenever refering to a graph we will be refering to an edge labeled graph. In this work we give a method to construct larger prime cordial graph using a. Conclusion labeling of discrete structure is a potential area of research.
Further we prove that the wheel graph wn admits prime cordial labeling for n. Graph labeling,sequential labeling, cordial labeling, total sequential cordial labeling tsc, path graph,and shadow graph. F, graph theory, adadisonwesley publishing company inc, usa, 1969. The cordial labeling concept was first introduced by cahit 2. A graph with a square divisor cordial labeling is called a square divisor cordial graph. Mean square cordial labeling on star related graphs iopscience. A graph g is called edge product cordial if it admits an edge product cordial labeling. Likewise, an edge labelling is a function of to a set of labels. A graph which admits a prime cordial labeling is called a prime cordial graph. We introduce acordial graphs, for an abelian group a. Cordial labeling of graphs 17 incident with z, delete from t vertices w. Furthermore, the program allows to import a list of graphs, from which graphs can be chosen by entering their. We investigate product cordial labeling for some new graphs. According to beineke and hegde 2 graph labeling serves as a frontier between number theory and structure of graphs.
The square divisor cordial labeling is a variant of cordial labeling and divisor cordial labeling. In the mathematical discipline of graph theory, a graph labelling is the assignment of labels, traditionally represented by integers, to edges andor vertices of a graph formally, given a graph, a vertex labelling is a function of to a set of labels. These generalize harmonious, elegant, and cordial graphs. One of the important areas in graph theory is graph labeling. The field of graph theory plays vital role in various fields. This work aims to dispel certain longheld notions of a severe psychological disorder and a wellknown graph labeling conjecture. For a graph g the splitting graph s g of a graph g is obtained by adding a new vertex v corresponding to each vertex v of g such that nv nv. The vertex set and edge set of a graph g is denoted by vg and. The technique by which a graph is labeled can be applied on coding theory, missile guidance. We show that trees are 3, 4 and 5cordial and provide a finite though long test that, if passed, guarantees that all trees are a. Simple logic problems dont pose much of a challenge, but applying some graph theory can help to solve much larger, more complex problems. Eg 0,1 is called an edge product cordial labeling of graph g, if the in duced vertex labeling.
The origin of graph labelings can be attributed to rosa 3. Star of swastik graph s wn is cordial, where n 2n f 1g. An example usage of graph theory in other scientific. A binary vertex labeling of graph g is called a product cordial labeling if jv f 0 v f 1j 1 and je f 0 e f 1j 1. A graph with a mean cordial labeling is called a mean cor dial graph. Gallian 1 has given a dynamic survey of graph labeling. A graph g is cordial if it admits cordial labeling. Theory and applications graph labelings, where the vertices and edges are assigned, real values subject to certain conditions, have often been motivated by their utility to various applied fields and their intrinsic mathematical interest logico mathematical. In this work, a discussion is made on shell, tensor product, coconut tree, jelly fish and subdivision of bistar under square divisor cordial labeling. A prime cordial labeling of a graph g with vertex set v is a bijection f from v to 1, 2. Above labeling patten give rise a cordial labeling to cycle of r copies for swastik graph illustration 2. A cycle of four copies for s w2 and its cordial labeling theorem 2. Labeled graphs serve as useful models for a wide range of applications.
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