Distance magic labeling of join of graphs and big data analysis

Abstract

Consider a simple graph G = 〈V, E〉 with n vertices. Define a function f from vertex set of G to set of integers 1, 2, …, n subject to the condition that there exists an integer k > 0 such that the sum of adjacent labels of each vertex in G is equal to k. In this paper, we prove that the graph K n - ⌊ n 2 ⌋ e has DML for all n ≥ 1, decomposition of distance magic graph K2n - {ne} into n ( n - 1 ) 2 edge distinct copies of C4 for all n ≥ 2 and DML of join of complete graphs gives unique mathematical model and it will be a useful model in big data analysis.