It is known that if an almost bipartite graph G with n edges possesses a γlabeling, then the complete graphK2nx+1 admits a cyclicG-decomposition. We introduce a variation of γ-labeling and show that whenever an almost bipartite graph G admits such a labeling, then there exists a cyclic Gdecomposition of a family of circulant graphs. We also determine which odd length cycles admit the variant la...

For each positive integer \(k\), a simple graph \(G\) of order \(p\) is said to be \(k\)-prime labeling if there exists an injective function \(f\) whose labels are from \(k\) \(k+p-1\) that induces \(f^{+}:E(G)\to N\) the edges defined by \(f^{+}(uv)=\gcd(f(u),f(v))\), \(\forall\) \(e=uv \in E(G)\) such every pair neighbouring vertices relatively prime. This type known as graph. In this paper,...

An injective function f : V pGq Ñ t0, 1, 2, . . . , qu is an odd sum labeling if the induced edge labeling f defined by f puvq fpuq fpvq, for all uv P EpGq, is bijective and f pEpGqq t1, 3, 5, . . . , 2q 1u. A graph is said to be an odd sum graph if it admits an odd sum labeling. In this paper we study the odd sum property of graphs obtained by duplicating any edge of some graphs.

A coprime labeling of a simple graph of order n is a labeling in which adjacent vertices are given relatively prime labels, and a graph is prime if the labels used can be taken to be the first n positive integers. In this paper, we consider when ladder graphs are prime and when the corresponding labeling may be done in a cyclic manner around the vertices of the ladder. Furthermore, we discuss c...

A distance magic labeling of a graph G = (V, E) of order n is a bijection l : V → {1, 2, . . . , n} with the property that there is a positive integer k (called magic constant) such that w(x) = k for every x ∈ V . If a graph G admits a distance magic labeling, then we say that G is a distance magic graph. In the case of non-regular graph G, the problem of determining whether there is a distance...

A labeling of a graph is a function from the vertex set of the graph to some finite set. Certain dynamical systems (such as topological Markov shifts) can be defined by directed graphs. In these instances, a labeling of the graph defines a continuous, shift-commuting factor of the dynamical system. We find sufficient conditions on the labeling to imply classification results for the factor dyna...

We introduce new labeling called m-bonacci graceful labeling. A graph G on n edges is if the vertices can be labeled with distinct integers from set {0,1,2,…,Zn,m} such that derived edge labels are first numbers. show complete graphs, bipartite gear triangular grid and wheel graphs not graceful. Almost all trees give to cycles, friendship polygonal snake double graphs.

Abstract. A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,... | |} V such that an edge uv is assigned the label 1 if ( ) | ( ) f u f v or ( ) | ( ) f v f u and the label 0 otherwise, then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a divisor cordial labeling is called a divisor cordial graph. ...

Graphs form a powerful modeling tool to represent complex relationships among objects in an effective manner. Graph pattern matching is one of the areas of data mining where the data is stored in the form of graphs and the set of tuples that match a user-given graph pattern are extracted. For finding the set of matching tuples faster, all the possible paths in the large directed graph, i.e., tr...

A labeling of a graph is a bijective function onto its edges from the set {1, 2, . . . , |E(G)|}. A labeling is antimagic if for every pair of distinct vertices u and v, the sum of the labels on edges incident to u is different from the sum of the labels on edges incident to v. We say a graph is antimagic if it has an antimagic labeling. In 1990, Ringel conjectured that every connected graph ot...