Manuscript Number : CSEIT1724163
A Study on Magic Labeling Regular Graph
Authors(2) :-P. Vivegananthan , B. Senthilkumar Let G(V, E) be a graph and λ be a bisection from the set V ∪ E to the set of the first |V | + |E| natural numbers. The weight of a vertex is the sum of its label and the labels of all adjacent edges. We say λ is a vertex magic total (VMT) labeling of G if the weight of each vertex is constant. We say λ is an (s, d) -vertex anti-magic total (VAT) labeling if the vertex weights form an arithmetic progression starting at s with difference d . J. MacDougall conjectured that any regular graph with the exception of K2 and 2K3 has a VMT labeling. We give constructions of VAT labelings of any even-regular graphs and VMT labelings of certain regular graphs.
P. Vivegananthan Graph Labeling, Vertex Magic Total Labeling, Vertex Antimagic Total Labeling. Publication Details Published in : Volume 2 | Issue 4 | July-August 2017 Article Preview
Department of Mathematics, PRIST University, Thanjavur, Tamil Nadu, India
B. Senthilkumar
Department of Mathematics, PRIST University, Thanjavur, Tamil Nadu, India
Date of Publication : 2017-08-31
License: This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 615-620
Manuscript Number : CSEIT1724163
Publisher : Technoscience Academy