Study Of The Problem Of The Spectral Radius Of A Kind Of Starlike Tree

Graph theory is an important branch of combination mathematics. It has been applied inmany different fields in the modern world, such as physics, chemistry, astronomy, geography,biology, as well as in computer science and engineering.In this thesis, it mainly studied the spectrum of the starlike tree. Hong Yuan who firstlystudied the relationship between graphs and its eigenvalue, obtained all the spectra radius ofthe trees whose radius are not upper k and the graphs achieved the spectral radius.First, it mainly studies the extremal graphs of the starlike trees with maximal degree4,and the lower and upper bounds of spectral radius is Calculated. Extremal graphs of the graphare obtained by using "moving edge" transforms. Then used in element method to solve thecharacteristic polynomial. The upper bound of the4-starlike tree can be obtained is2, andlower bound of the tree is4/3. This method is extended to the study of spectral radius ofk-starlike tree. The extremal graphs of the graph are also obtained by using "moving edge"transforms. Adjacency matrix of4-strarlike tree is generated by using Matlab programming.Let n be a variable. When n is large enough the upper bound of the4-starlike tree is found.The accuracy of the identified is proved. Adjacency matrix of strarlike tree with differentmaximum degree is generated by using Matlab programming. Then observe the changes ofspectral radius throw the changing of maximum degree changing.Secondly the spectrum of the starlike tree with two maximal degree is studied. Theregularity of4-double-starlike tree spectrum is found and the lower and upper bounds ofspectral radius is also Calculated. The upper bound and lower bound of the tree is obtained.Adjacency matrix of double-strarlike tree is generated by using Matlab programming. Theaccurate spectral radius is get. The above method is used in study of k-double-starlike tree.