Some bounds on the largest eigenvalues of graphs

Bounds on the Largest of Minimum Degree Eigenvalues of Graphs

Let G be a simple graph and let its vertex set be V (G) = {v1, v2, ..., vn}. The adjacency matrix A(G) of the graph G is a square matrix of order n whose (i, j)-entry is equal to unity if the vertices vi and vj are adjacent, and is equal to zero otherwise. The eigenvalues λ1, λ2, ..., λn of A(G), assumed in non increasing order, are the eigenvalues of the graph G. The energy of G was first defi...

On the bounds for the largest Laplacian eigenvalues of weighted graphs

On the distance eigenvalues of Cayley graphs

In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...

On the eigenvalues of non-commuting graphs

The non-commuting graph $Gamma(G)$ of a non-abelian group $G$ with the center $Z(G)$ is a graph with thevertex set $V(Gamma(G))=Gsetminus Z(G)$ and two distinct vertices $x$ and $y$ are adjacent in $Gamma(G)$if and only if $xy neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.

Bounds on normalized Laplacian eigenvalues of graphs

*Correspondence: [email protected] 1School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian, P.R. China 2Center for Discrete Mathematics, Fuzhou University, Fuzhou, Fujian, P.R. China Full list of author information is available at the end of the article Abstract Let G be a simple connected graph of order n, where n≥ 2. Its normalized Laplacian eigenvalues are 0 = λ1 ...