The spectral radius of the adjacency matrix of a complete binary tree as the number of nodes approaches infinity

Abstract

Trees are connected graphs without cycles, which are widely used in different fields. One of the hot topics in graph theory is the eigenvalue of graph's adjacency matrix, also known as graph's adjacency spectrum, which is an important research field of graph theory and has a wide range of practical applications. In this paper, we prove that the spectral radius of the adjacency matrix of the complete binary tree is 2√2 when the number of nodes tends to infinity by the eigenvalue of the adjacency matrix of the complete binary tree.