Given a connected regular graph G, let l (G) be its line graph, s (G) its subdivision graph, r
(G) the graph obtained from G by adding a new vertex corresponding to each edge of G and …

Let L n be a linear hexagonal chain with n hexagons. In this paper, according to the
decomposition theorem of normalized Laplacian polynomial of a graph, we obtain that the …

Let W n be a linear pentagonal chain with 2 n pentagons. In this article, according to the
decomposition theorem for the normalized Laplacian polynomial of W n, we obtain that the …

Let G be a simple connected graph of order n, where n≥ 2. Its normalized Laplacian
eigenvalues are 0= λ 1≤ λ 2≤⋯≤ λ n≤ 2. In this paper, some new upper and lower bounds …

The quadrilateral graph Q (G) of G is obtained from G by replacing each edge in G with two
parallel paths of lengths 1 and 3. In this paper, we completely describe the normalized …

The eigenvalues of a graph present a wide range of applications in structural and dynamical
aspects of the graph. Determining and analyzing spectra of a graph has been an important …

We define a (pseudo-) distance between graphs based on the spectrum of the normalized
Laplacian. Since this quantity can be computed easily, or at numerically estimated, it is …

The k-triangle graph T k (G) is obtained from a graph G by replacing each edge in G with k+
1 parallel paths, in which one is of length 1 and each of the rest k paths is of length 2; …

A novel distance function named resistance distance was introduced on the basis of
electrical network theory. The resistance distance between any two vertices u and v in graph …

Various structural and dynamical properties of a network are encoded in the eigenvalues of
walk matrix describing random walks on the network. In this paper, we study the spectra of …