Research On Some Kinds Of Energy Of Graphs

Spectral theory of graphs as an important branch of algebraic graph theory,it mainly concerns the relation between the combinatorial properties of a graph and the algebra-ic properties of matrices(such as adjacency matrix,Laplacian matrix,incidence matrix,etc.)associated with the graph.It has broad but important application in physics,quan-tum chemistry,information science and communication networks and so on.This thesis does some researches on Laplacian-energy-like invariant of H-join graph-s,Laplacian sptrctra SpecL(G)(Signless Laplacian sptrctra SpecQ(G))of variants of the corona of two graphs,some kinds of energy of mixed graphs,obtains some new mean-ingful results,and consists of the following four chapters.In Chapter 1,besides introducing some background and developments of the graph energy,some fundamental concepts,which will be used later,we list the main results of this thesis.In Chapter 2,under certain conditions,we discuss the upper and lower bounds of Laplacian-energy-like invariant for H-join graphs.In Chapter 3,we mainly describe the Laplacian sptrctra(Signless Laplacian sptrctra)of the following two kinds of(Gi V G2)?(G1?G3)?(G1 V GZ)?(GZ ? G3)?(G1 ? G4).In Chapter 4,firstly,we discuss the relationship among the Hermitian energy ?H(M)of mixed graphs the energy ?A(Mu)of underlying graph Mu for mixed graphs M and the skew energy ?s(G?)of oriented graph G? for underlying graph Mu.Secondly,on the construction method of a class of Hermitian equienergetic graphs and the Hermitian en-ergy bound of M.Lastly,we study the spectral properties of the Hermite-quasi-Laplacian matrix Q(M)of mixed graphs,by using the number of its vertices,the number of it-s edges and maximum degree,we gives bounds of Hermitian incidence energy of the mixed graph.