A STUDY ON TOTALLY MAGIC GRAPH

Author (s) : M.ISHWARYA, C.KARUNAIVELAN, R. SATHYASHANTHI

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Abstract :
Magic graphs are related to the well-known magic squares, but are not quite as famous. These mathematical puzzles are known to people for more than 4000 years, but no sooner than in than in the 1960s it was tired to apply this concept to graphs.The goal of this master-thesis is to carry out a complete search for totally magic graphs among all graphs with 11 vertices. It thereby continues the work by which investigated all graphs with 10 or less vertices. The difficulty of the search among all graphs with 11 vertices is its complexity. The total deficiency of a totally magic injection with maximum label M is M-│V│-│E│. A totally magic injection with deficiency 0 is called a totally magic labeling. Labeling where the vertices are assigned real values subject to certain conditions, have often been motivated by practical problems, but they are also of mathematical interest in their own.  An enormous body of literature has grown around the subject, especially in the last thirty years or so, and is presented in a survey. A(p,q)-graph G=(V,E) is said to be magic if there exists a bijection f:VUE →{1,2,3,… ,p+q} such that foe all edges uv of G,f(u)+ f(v)+ f(uv) is a constant. Such a bijection is called magic label

Keywords : Graphs, Totally magic, Edge Total magic labeling, Vertex magic labeling.

Conference Date : 13/11/2020

Pages : 99

Paper ID : 20099