On The Spectral Moment Of Graphs With K Cut Edges

For a connected graph G, let A(G) be the adjacency matrix of a graph G with λ1(G), λ2(G),..., λn(G) being the eigenvalues in non-increasing order. Call the number Sk(G):=Σ(i=1)nλik(G),(k=0,1,..., n-1) the kth spectral moment of G. Let S(G)=(S0(G),S1(G),...,Sn-1(G)) be the sequence of spectral moments of G. For two graphs G1and G2, we have G1-<s G2(G1comes before G2in an S-order) if Si(G1)=Si(G2)(i=0,1,...,k:-1) and Sk(G1)<Sk(G2) for some k E{1,2,...,n-1}. Denote by&Gnk the set of connected n-vertex graphs with k cut edges. The concrete content is in the following:●In chapter1, we introduce the background and significance of the research, in-cluding the development of a representative at home and abroad regarding this aspect. Based on this research background and profound discussion, by using deep-going analysis, it fully shows the main work’s necessity and innovation.●In chapter2, we give some necessary definition and lemmas.●In chapter3, we determine the last two graphs in S-rder among connected graphs with k cut edges.●In chapter4, we determine the first two graphs in S-rder among connected graphs with k cut edges.●In chapter5, we summary the paper and give prospects in the future.