A connected graph G=(V, E) is called a quasi-tree, if there exists u0∈ V (G) such that G-u0 is
a tree. Denote Q (n, d0)={G: G is a quasi-tree graph of order n with G-u0 being a tree and dG …

Let $ A (G) $ be the adjacency matrix of a graph $ G $ with $\lambda_ {1}(G) $, $\lambda_
{2}(G) $,..., $\lambda_ {n}(G) $ being its eigenvalues in non-increasing order. Call the …

Lexicographic ordering by spectral moments (S-order) among all trees is discussed in this
paper. For integers n and k, let p (n, k) be the number of all partitions of n into k parts. The …

The lexicographical ordering of hypergraphs via spectral moments is called the $ S $-order
of hypergraphs. In this paper, the $ S $-order of hypergraphs is investigated. We …

The k-th spectral moment M k (G) of the adjacency matrix of a graph G represents the
number of closed walks of length k in G. We study here the partial order≼ of graphs, defined …

Suppose G is a graph, A (G) its adjacency matrix, and μ1 (G)≤ μ2 (G)≤…≤ μ n (G) are
eigenvalues of A (G). The numbers Sk (G)=(Σ i= 1 n μ ik (G), 0≤ k≤ n− 1 are said to be the k …

Let L_n,t be the set of all n-vertex connected graphs with clique number t (2≦t≦n). For n-
vertex connected graphs with given clique number, lexicographic ordering by spectral …

Lexicographic ordering by spectral moments ($ S $-order) among all trees is discussed in
this‎‎ paper‎.‎ For two given positive integers $ p $ and $ q $ with $ p\leqslant q $‎,‎ we denote …

Suppose $ G $ is a graph, $ A (G) $ its adjacency matrix, and $ μ_1 (G), μ_2 (G),\cdots, μ_n
(G) $ are eigenvalues of $ A (G) $. The numbers $ S_k (G)=\sum_ {i= 1}^ n μ^ k_i (G) …

For two given positive integers $ p $ and $ q $ with $ p\leqslant q $, 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 …