Given an arbitrary connected $G$, the $n$-polygon graph $\tau_n(G)$ is obtained by adding a path with length $n$ $(n\geq 2)$ to each edge of graph $G$, and the iterated $n$-polygon graphs $\tau_n^g(G)$ ($g\geq 0$), is obtained from the iteration $\tau_n^g(G)=\tau_n(\tau_n^{g-1}(G))$, with initial condition $\tau_n^0(G)=G$. In this paper, a method for calculating the eigenvalues of normalized Laplacian matrix for graph $\tau_n(G)$ is presented if the eigenvalues of normalized Laplacian matrix for graph $G$ is given firstly. Then, the normalized Laplacian spectrums for the graph $\tau_n(G)$ and the graphs $\tau_n^g(G)$ ($g\geq 0$) can also be derived. Finally, as applications, we calculate the multiplicative degree-Kirchhoff index, Kemeny's c...
A graph G is called integral or Laplacian integral if all the eigenvalues of the adjacency matrix A(...
As a generalization of the Sierpiński-like graphs, the subdivided-line graph Г(G) of a simple connec...
For a simple and connected graph, a new graph invariant s(G), defined as the sum of alpha-powers of ...
Determining and analyzing the spectra of graphs is an important and exciting research topic in mathe...
The eigenvalues of the normalized Laplacian of a graph provide information on its topological and st...
The normalized Laplacian plays an important role on studying the structure properties of non-regular...
AbstractIn this paper we study the Laplacian spectra, the Laplacian polynomials, and the number of s...
To any graph we may associate a matrix which records information about its structure. The goal of sp...
AbstractWe investigate how the spectrum of the normalized (geometric) graph Laplacian is affected by...
Let G be a graph. The Laplacian matrix L(G)=D(G) -A)(G) is the difference of the diagonal matrix of ...
summary:Let $G$ be a graph with $n$ vertices, $m$ edges and a vertex degree sequence $(d_1, d_2, ...
AbstractLet M denote the Laplacian matrix of a graph G. Associated with G is a finite group Φ(G), ob...
Let G be a finite simple graph with vertex set V(G) = {v1, v2, v3, …, vn} and edge set E(G). The adj...
AbstractWe show that, in the graph spectrum of the normalized graph Laplacian on trees, the eigenval...
In this paper we determine the full normalized Laplacian spectrum of the subdivision-vertex join, su...
A graph G is called integral or Laplacian integral if all the eigenvalues of the adjacency matrix A(...
As a generalization of the Sierpiński-like graphs, the subdivided-line graph Г(G) of a simple connec...
For a simple and connected graph, a new graph invariant s(G), defined as the sum of alpha-powers of ...
Determining and analyzing the spectra of graphs is an important and exciting research topic in mathe...
The eigenvalues of the normalized Laplacian of a graph provide information on its topological and st...
The normalized Laplacian plays an important role on studying the structure properties of non-regular...
AbstractIn this paper we study the Laplacian spectra, the Laplacian polynomials, and the number of s...
To any graph we may associate a matrix which records information about its structure. The goal of sp...
AbstractWe investigate how the spectrum of the normalized (geometric) graph Laplacian is affected by...
Let G be a graph. The Laplacian matrix L(G)=D(G) -A)(G) is the difference of the diagonal matrix of ...
summary:Let $G$ be a graph with $n$ vertices, $m$ edges and a vertex degree sequence $(d_1, d_2, ...
AbstractLet M denote the Laplacian matrix of a graph G. Associated with G is a finite group Φ(G), ob...
Let G be a finite simple graph with vertex set V(G) = {v1, v2, v3, …, vn} and edge set E(G). The adj...
AbstractWe show that, in the graph spectrum of the normalized graph Laplacian on trees, the eigenval...
In this paper we determine the full normalized Laplacian spectrum of the subdivision-vertex join, su...
A graph G is called integral or Laplacian integral if all the eigenvalues of the adjacency matrix A(...
As a generalization of the Sierpiński-like graphs, the subdivided-line graph Г(G) of a simple connec...
For a simple and connected graph, a new graph invariant s(G), defined as the sum of alpha-powers of ...