Dendrimer Growth Based on Algebraic Multiplicity

Abstract

Matching Theory is one of the important concepts of Graph Theory. The matching theory concept has been studied in many areas. In this paper, the growth of Dendrimer through the maximum matching of an undirected sparse graph based on algebraic multiplicity of its eigenvalues is studied. The matrix adjacency of an undirected Dendrimer is a sparse graph and it is related to the exact controllability network for finding the maximum matched nodes and the corresponding match edges using the largest algebraic multiplicity of eigenvalues. The growth of the Dendrimer is expanded to nth- generation and the molecular formula is calculated. The process of finding the maximum matching starts initially from the core molecule and extended by adding branch molecule to the end groups at each stage of its growth forms the generation.