Super edge magic deficiencies of forests of alpha families of trees

Abstract

Let G be a graph which is admitting an edge-magic total valuation. The edge magic deficiency [38] of this graph G is the positive numbers α required to make it a edge magic total graph. The general notation for edge-magic deficiency is μ(G). If there does not exist such α then edge magic deficiency will be ∞. The super edge magic deficiency of graph G [17], follows the same definition and it is denoted by μs(G). This dissertation studies about the super edge-magic deficiencies of forests of alpha families of trees. Firstly, We show that alpha trees with caterpillars as its components have super edge-magic deficiency is μs = 0. We also prove that if the alpha tree has w-trees and alpha trees as its components then its super edge-magic deficiency is μs = 0. At the end, we prove that forest of alpha trees with components as banana tree and stars preserve super edge-magic deficiency μs = 1.