Let G be a connected graph and Q(G) the signless Laplacian of G. The principal ratio γ(G) is maximum minimum entries Perron vector Q(G). In this paper, we consider among all graphs order n, show that for sufficiently large n extremal kite obtained by identifying an end vertex path to any complete graph.

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 ...

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...