An eigenvalue μ of a graph G of order n is a main eigenvalue if its eigenspace is not
orthogonal to the all-ones vector e. Characterizing graphs with s (2≤ s≤ n) number of main …

In this paper, we consider the main eigenvalues of connected chain graphs. We provide
some properties of the eigenvectors corresponding to the main eigenvalues, upper and …

Let $\Gamma $ be a finite group acting transitively on $[n]=\{1, 2,\ldots, n\} $, and let $
G=\mathrm {Cay}(\Gamma, T) $ be a Cayley graph of $\Gamma $. The graph $ G $ is called …

A few examples and counterexamples in spectral graph theory Page 1 Discussiones
Mathematicae Graph Theory 40 (2020) 637–662 doi:10.7151/dmgt.2275 A FEW …

An eigenvalue of the adjacency matrix of a graph is said to be main if the all-1 vector is non-
orthogonal to the associated eigenspace. This paper explores some new aspects of the …

The first and the second Zagreb index of a graph, usually defined as the sum of the squares
of degrees over all vertices and the sum of the products of degrees of edge endvertices over …

Let G (resp. G n) be the set of connected graphs (resp. with n vertices) whose eigenvalues
are mutually distinct, and G∗(resp. G n∗) the set of connected graphs (resp. with n vertices) …

设是一个符号图, 的特征值是其邻接矩阵的特征值. 设是的一个特征值, 如果存在属于的一个特征
向量, 使得, 则称是的主特征值. 图的主特征值为研究图的性质和图的其它不变量都有重要的意义 …

Let G be a graph. For a subset X of V (G), the switching σ of G is the signed graph G σ
obtained from G by reversing the signs of all edges between X and V (G)∖ X. Let A (G σ) be …

An eigenvalue of the adjacency matrix of a graph is said to be main if the all-ones vector is
not orthogonal to its associated eigenspace. In this paper, we investigate the main …