Total magic cordial labeling of star related graph

Abstract

A star S n is a complete bipartite graph K 1n also known as n-star is a tree with one vertex with n-1 degree and other vertices with 1 degree. The Bistar B m , n is a graph obtained from K 2 by joining m pendant edges to one vertex of K 2 and n pendent edges to the other vertex of K 2 . The vertices of K 2 are called the central vertices of B m , n and the edge of K 2 is called the central edge of B m , n . In this paper we prove that star, split of star, Bistar and split of bistar admits total magic cordial labeling, where it is defined as a mapping from the set of vertices and edges to the integers {0,1} such that a sum of the label of an edge and its end vertices is equal to a constant congruent to mod 2, subject to the condition that the absolute value of f 0 and f 1 differ at most by one, where f0 is the sum of vertices and edges labeled zero and f 1 is the sum of vertices and edges labeled one. AMS Subject Classification: 05C78.