The Spectral Radius Of Tricyclic Graphs

The spectral radius of a graph is defined as the largest eigenvalue of its adjacency matrix.With the wider use of it in graph spectra in recent years,the research concerning about this aspect have mushroomed like an endless stream.This paper which stands on the basis of previous results,and which further research on the issue of the spectral radius of tricyclic graphs,mainly includes:·It introduces the paper's research background and significance;including the development of a representative at home and abroad regarding this aspect. Based on this research background and profound discussion on the status quo, it fully shows the main work's necessity and innovation.·We study the spectral radius of tricyclic graphs on n vertices with k pendent vertices.The n-vertex tricyclic graph with k pendent vertices having maximum spectral radius is characterized.·The spectral radius of tricyclic graphs with n vertices and diameter d is studied. The n-vertex tricyclic graph with of given diameter d with maximum spectral radius is determined.·We also study the spectral radius of tricyclic graphs on n vertices with perfect matchings.The 2m-vertex tricyclic graph with with perfect matchings have maximum spectral radius is determined.