Let G be a simple graph with eigenvalues λ1, λ2, . . . , λn. The Estrada index of G is defined as EE(G) = ∑ n i=1 ei . In this paper, the unique graph with maximum Estrada index is determined among connected graphs with given numbers of vertices and cut edges.

Several hundreds of so-called molecular structuredescriptors were proposed in the chemical literature [1] and are used for modeling of various physical and chemical properties of (mainly) organicmolecules. In general, a molecular structure-descriptor is a number, usually computed from the molecular graph [2, 3], that reflects certain topological features [4, 5] of the underlying molecule. Many ...

Let λ1, λ2, · · · , λn be the eigenvalues of the distance matrix of a connected graph G. The distance Estrada index of G is defined as DEE(G) = ∑ n i=1 ei . In this note, we present new lower and upper bounds for DEE(G). In addition, a Nordhaus-Gaddum type inequality for DEE(G) is given. MSC 2010: 05C12, 15A42.

Several researchers have recently explored various graph parameters that can or cannot be characterized by the spectrum of a matrix associated with graph. In this paper, we show several NP-hard zero forcing numbers are not spectra types matrices particular, consider standard forcing, positive semidefinite and skew provide constructions infinite families pairs cospectral graphs, which different ...

The universal adjacency matrix U of a graph Γ, with A, is linear combination the diagonal D vertex degrees, identity I, and all-1 J real coefficients, that is, U=c1A+c2D+c3I+c4J, ci∈R c1≠0. Thus, in particular cases, may be matrix, Laplacian, signless Seidel matrix. In this paper, we develop method for determining spectra bases all corresponding eigenspaces arbitrary lifts graphs (regular or no...

Given V a finite set, a self–adjoint operator on C(V ), K, is called elliptic if it is positive semi–definite and its lowest eigenvalue is simple. Therefore, there exists a unique, up to sign, unitary function ω ∈ C(V ) satisfying K(ω) = λω and then K is named (λ, ω)–elliptic. Clearly, a (λ, ω)–elliptic operator is singular iff λ = 0. Examples of elliptic operators are the so–called Schrödinger...