Thewheel graph, denoted byWn+1, is the graph obtained from the circuit Cn with n vertices by adding a new vertex and joining it to every vertex of Cn. In this paper, the wheel graph Wn+1, except for W7, is proved to be determined by its Laplacian spectrum, and a graph cospectral with the wheel graphW7 is given. © 2009 Elsevier Ltd. All rights reserved.

In this article, we relate the spectrum of discrete magnetic Laplacian (DML) on a finite simple graph with two structural properties graph: existence perfect matching and Hamiltonian cycle underlying graph. particular, give family spectral obstructions parametrised by potential for to be matchable (i.e., having matching) or cycle. We base our analysis special case preorder introduced in [8], us...

The spectrum of the Laplacian of successive Barycentric subdivisions of a graph converges exponentially fast to a limit which only depends on the clique number of the initial graph and not on the graph itself. Announced in [40]), the proof uses now an explicit linear operator mapping the clique vector of a graph to the clique vector of the Barycentric refinement. The eigenvectors of its transpo...

We consider a family of compact manifolds which shrinks with respect to an appropriate parameter to a graph. The main result is that the spectrum of the Laplace-Beltrami operator converges to the spectrum of the (differential) Laplacian on the graph with Kirchhoff boundary conditions at the vertices. On the other hand, if the shrinking at the vertex parts of the manifold is sufficiently slower ...

In a recent paper Gunnells, Scott and Walden have determined the complete spectrum of the Schreier graph on the symmetric group corresponding to the Young subgroup Sn−2 × S2 and generated by initial reversals. In particular they find that the first nonzero eigenvalue, or spectral gap, of the Laplacian is always 1, and report that “empirical evidence” suggests that this also holds for the corres...

Let Gr,p be a graph obtained from a path by adjoining a cycle Cr of length r to one end and the central vertex of a star Sp on p vertices to the other end. In this paper, it is proven that unicyclic graph Gr,p with r even is determined by its Laplacian spectrum except for n = p+4.

Let G be a simple connected graph with n ≤ 2 vertices and m edges, and let μ1 ≥ μ2 ≥...≥μn-1 >μn=0 be its Laplacian eigenvalues. The Kirchhoff index and Laplacian-energy-like invariant (LEL) of graph G are defined as Kf(G)=nΣi=1n-1<...

Let Γ = (G,σ) be a signed graph, where σ is the sign function on edges of G. In this paper, we use operation partial transpose to obtain non-isomorphic Laplacian cospectral graphs. We will introduce two new operations These establish relationship between adjacency spectrum one graph with another graph. As an application, these utilized construct several pairs Finally, integral