Estimation Of P-Laplacian Spectrum For Several Special Graphs

Graph spectrum,including the Laplacian spectrum,the adjacent spectrum and the signless Laplacian spectrum of graphs,etc.,becomes an important area of algebraic graph theory.In recent years,in order to solve some problems in machine learning and other fields,the concept of p-Laplacian spectrum has been posed and studied by many scholars.The main focus of this paper are on some bounds of eigenvalue and spectrum of p-Laplacian of some special graphs.The works of this paper are as follows:1.On the basis of the upper bound of the Laplacian eigenvalue of connected graphs given by Li Jiongsheng and Pan Yongliang,we apply Absolute value inequality and Jensen inequality to obtain the two upper bounds of the p-Laplacian eigenvalue of connected graphs,and compare the two upper bounds with given by S.Amghibech.2.We study the structural characteristics of a class of single circle graphs,and we obtain the upper and lower bounds of p-Laplacian eigenvalues of these graphs by using Absolute value inequality and Jensen inequality.These bounds improve the results of general connected graphs given by S.Amghibech.3.For wheel graphs,we obtain the upper bound of p-Laplacian by using Absolute value inequality,Jensen inequality and Minknowski inequality,which improves the result of general connected graph given by S.Amghibech.4.By using the properties of lollipop graphs,we obtain the upper and lower bounds of p-Laplacian of the graphs.These upper and lower bounds improve the results of general connected graphs given by S.Amghibech.