- Publication venue
- Publication date
- 20/11/2012
- Field of study
For two given positive integers p and q with pβ©½q, we denote
\mathscr{T}_n^{p, q}={T: T is a tree of order n with a (p,q)-bipartition}. For a graph G with n vertices, let A(G) be its
adjacency matrix with eigenvalues Ξ»1β(G),Ξ»2β(G),...,Ξ»nβ(G) in non-increasing order. The number
Skβ(G):=βi=1nβΞ»ikβ(G)(k=0,1,...,nβ1) is called the kth
spectral moment of G. Let S(G)=(S0β(G),S1β(G),...,Snβ1β(G)) be the
sequence of spectral moments of G. For two graphs G1β and G2β, one has
G1ββΊsβG2β if for some kβ1,2,...,nβ1, Siβ(G1β)=Siβ(G2β)(i=0,1,...,kβ1) and Skβ(G1β)<Skβ(G2β) holds. In this paper, the last four
trees, in the S-order, among Tnp,qβ(4β©½pβ©½q)
are characterized.Comment: 11 pages, 7 figure