F, graph theory, adadisonwesley publishing company inc, usa, 1969. If g is a graph, then a vertex labeling function f. 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. Labeled graphs serve as useful models for a wide range of applications. G maxfdv j v 2 vg is the maximum degree of the vertices in the graph g. 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. Corollary if g is 3 edge sum cordial graph then it is 3total edge sum cordial labeling of graph. A graph g is called edge product cordial if it admits an edge product cordial labeling. A graph g is product cordial if it admits product cordial labeling. The cordial labeling concept was first introduced by cahit 2.
Pdf some more sum divisor cordial labeling of graphs. Cordial labeling for the splitting graph of some standard graphs 107 2 main results theorem 2. 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. Gallian 1 has given a dynamic survey of graph labeling. A graph is called cordial if it is possible to label its vertices with 0s and 1s so. We prove that the friendship graph, cycle with one chord except when n is even and the chord joining the vertices at diameter distance. Graph theory has a good development in the graph labeling and has a broad range of applications. 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 concept of cordial labeling was introduced by cahit 1. 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. One of the important areas in graph theory is graph labeling.
Further we prove that the wheel graph wn admits prime cordial labeling for n. In this paper an analysis is made on union of graphs are prime cordial labeling. The field of graph theory plays an important role in various areas of pure. Graph theory software to at least draw graph based on the program. Simple logic problems dont pose much of a challenge, but applying some graph theory can help to solve much larger, more complex problems. Rosa, on certain valuations of the vertices of a graph, theory of. Graph labeling connects many branches of mathematics and is considered one of important blocks of graph theory, for more details see 3. 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. The following graphs are proved as prime cordial labeling. The resulting tree t has n 2 vertices, and so by induction hypothesis it admits a cordial labeling, say f. The concept of cordial labeling was introduced by cahit 1 in which he proved that the wheel w.
A prime cordial labeling of a graph g with vertex set v is a bijection f from v to 1,2. We have investigated 3total edge sum cordial labeling of graphs to. A graph with a mean cordial labeling is called a mean cor dial graph. A graph with a square divisor cordial labeling is called a square divisor cordial graph. Cordial labeling of graphs 17 incident with z, delete from t vertices w.
The square divisor cordial labeling is a variant of cordial labeling and divisor cordial labeling. 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. Introduction the eld of graph theory plays a vital role in various elds. Square difference labeling, square difference graph. 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. Likewise, an edge labelling is a function of to a set of labels. In this work we give a method to construct larger prime cordial graph using a. Star of swastik graph s wn is cordial, where n 2n f 1g. 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. A free graph theory software tool to construct, analyse, and visualise graphs for science and teaching. Applications of graph labeling in communication networks.
A graph having fibonacci cordial labeling is called fibonacci cordialgraph. Let ct n denote the onepoint union of tcycles of length n. A prime cordial labeling of a graph g with vertex set v is a bijection f from v to 1, 2. A graph with such a labeling is an edge labeled graph. A graph g is cordial if it admits cordial labeling. In this paper, i inspect the existence of fibonacci cordial labeling of dspn,dsdfn,edgeduplicationink 1, n,jointsum ofgln,dfn. The origin of graph labelings can be attributed to rosa 3. The concept of cordial graphs was introduced by cahit3. We investigate mean cordial labeling behavior of paths, cycles, stars, complete graphs, combs and some more standard graphs. Pdf cordial labeling for the splitting graph of some standard.
Keywords graph labeling, duplicate graph, triangular ladder, bistar, double star, signed product cordial labeling. In this paper we investigate product cordial labeling for some new graphs. We introduce acordial graphs, for an abelian group a. A sum divisor cordial labeling of a graph g with vertex set v is a bijection f from.
Mean square cordial labeling on star related graphs iopscience. Graph theory plays an important role for automatic graph generation in computer science technology applications such as database design, software engineering. According to beineke and hegde 2 graph labeling serves as a frontier between number theory and structure of graphs. A graph labeling is an assignment of labels to edges, vertices or both. Graph labeling,sequential labeling, cordial labeling, total sequential cordial labeling tsc, path graph,and shadow graph. On edge product cordial labeling of some product related. We investigate product cordial labeling for some new graphs. A graph which admits prime cordial labeling is called prime cordial graph. A graph with a difference cordial labeling is called a difference cordial graph. Here we prove that the graphs like flower fln, bistar bn,n, square graph of bn,n, shadow graph of. 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. Labeling constructions using digraph products sciencedirect. Cordial labelings were introduced by cahit 1987 as a weakened version of graceful and harmonious.
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. 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. The line graph lg of a graph g is the graph whose vertex set is. Prime and prime cordial labeling for some special graphs 1. Cordial and product cordial labeling for the extended. 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.
This work aims to dispel certain longheld notions of a severe psychological disorder and a wellknown graph labeling conjecture. Kragujevacjournalofmathematics volume4022016,pages290297. Conclusion labeling of discrete structure is a potential area of research. Prime cordial labeling of some wheel related graphs. 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 function from vertex set of a graph to the set 0, 1, which assigns the label f u. A graph which admits a prime cordial labeling is called a prime cordial graph. 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. Umbrella graph, p nqs n graph, c nq sn graphs are square difference graphs. 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. Kala, difference cordial labeling of graphs, global journal of mathematical sciences.
The technique by which a graph is labeled can be applied on coding theory, missile guidance. A graph gis said to be cordial if it admits a cordial labeling. T where each s i is a set of vertices having at least two vertices. For the remainer of this paper whenever refering to a graph we will be refering to an edge labeled graph.
Cordial labeling is one of the most interesting graph labeling. Vertex prime labeling,lcordial labeling,path,cycle. Introduction the concept of graph labeling was introduced by rosa in 1967 6. Sathish narayanan, further results on difference cordial labeling of corona graphs, the journal of the indian academy of mathematics, 3520. Above labeling patten give rise a cordial labeling to cycle of r copies for swastik graph illustration 2. These generalize harmonious, elegant, and cordial graphs. A graph with difference cordial labeling is called a difference cordial graph. A graph g is said to be quotient3 cordial graph if it receives quotient3 cordial labeling. 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.
Shobana the following graphs are proved as prime cordial labeling. The vertex set and edge set of a graph g is denoted by vg and. A prime cordial labeling of a graph g with the vertex set v g is a bijection f. In this paper we prove that the split graphs of k1,n and bn,n are prime cordial graphs. 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. A cordial labeling is a friendly labeling f for which c f. In this work, a discussion is made on shell, tensor product, coconut tree, jelly fish and subdivision of bistar under square divisor cordial labeling. Quotient 3 cordial labeling for star related graphs. Cordial labeling for the splitting graph of some standard.
Signed product cordial labeling in duplicate graphs of. For graph theoretic terminology, we refer to harary 2. 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. Introduction all graphs considered are finite, simple and undirected. Graph labeling is a very powerful tool that eventually makes. C4 s w2 and its cordial labeling shown in figure 3. A cycle of four copies for s w2 and its cordial labeling theorem 2. 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. An example usage of graph theory in other scientific. A binary vertex labeling of a graph g is called a cordial labeling if.
Furthermore, the program allows to import a list of graphs, from which graphs can be chosen by entering their. 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. Z, in other words it is a labeling of all edges by integers. Prime and prime cordial labeling for some special graphs.
Some edge product cordial graphs in the context of. Note that interchanging the vertex labels 0 and 1 in a cordial labeling results in a new cordial labeling of. They also provide a graphtheoretic realization of the function. The field of graph theory plays vital role in various fields.
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