In this paper, we discuss some properties of relations between a mixed graph and its line graph, which are used to characterize the Laplacian spectrum of a mixed graph. Then we present two sharp upper bounds for the Laplacian spectral radius of a mixed graph in terms of the degrees and the average 2-degrees of vertices and we also determine some extreme graphs which attain these upper bounds. ©...

Given a finite simple graph G, let G1 be its barycentric refinement: it is the graph in which the vertices are the complete subgraphs of G and in which two such subgraphs are connected, if one is contained into the other. If λ0 = 0 ≤ λ1 ≤ λ2 ≤ · · · ≤ λn are the eigenvalues of the Laplacian of G, define the spectral function F (x) = λ[nx] on the interval [0, 1], where [r] is the floor function ...

We derive several interesting formulae for the eigenvalues of the derangement graph and use them to settle affirmatively a conjecture of Ku regarding the least eigenvalue.

abstract let ‎g=(v,e) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎v‎‎‎ ‎and ‎edge ‎set ‎‎‎e. ‎the szeged index ‎of ‎‎g is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎g ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎if ‎‎‎‎s ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎v ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎s ‎of ‎size ‎3. ‎then ‎we ‎define ‎three ‎...

Several matrices can be associated to a graph such as the adjacency matrix or the Laplacian matrix. The spectrum of these matrices gives some informations about the structure of the graph and the question “Which graphs are determined by their spectrum?” remains a difficult problem in algebraic graph theory. In this article we enlarge the known families of graphs determined by their spectrum by ...

We develop eigenvalue estimates for the Laplacians on discrete and metric graphs using different types of boundary conditions at the vertices of the metric graph. Via an explicit correspondence of the equilateral metric and discrete graph spectrum (also in the “exceptional” values of the metric graph corresponding to the Dirichlet spectrum) we carry over these estimates from the metric graph La...

Let [Formula: see text], text] and be integers with text]. The set-inclusion graph is the whose vertex set consists of all text]- text]-subsets where two distinct vertices are adjacent if one them contained in other. In this paper, we determine spectrum automorphism group

the edge versions of reverse wiener indices were introduced by mahmiani et al. veryrecently. in this paper, we find their relation with ordinary (vertex) wiener index in somegraphs. also, we compute them for trees and tuc4c8(s) naotubes.

objectives: this study compared the effects of individual and group training on general health and stress of parents of children with autism spectrum disorders. methods: a sample of 75 parents of children referring to autistic children foundation (including 50 parents in two experimental groups and 25 parents in control group) was taken into account. sample parents were selected through accessi...