The spectrum of a Johnson graph is known to be given by the Eberlein polynomial. In this paper, a straightforward representation-theoretic derivation of this fact is presented. Also discussed are some consequences of this formula, such as the fact that infinitely many of them are Ramanujan. 1. Introduction. Johnson graphs are heavily studied objects. The spectrum of any graph—that is, the multi...

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 ...

An oriented graph G is a simple undirected graph G with an orientation σ, which assigns to each edge a direction so that G becomes a directed graph. G is called the underlying graph of G, and we denote by Sp(G) the adjacency spectrum of G. Skew-adjacency matrix S(G) of G is introduced, and its spectrum SpS(G ) is called the skew-spectrum of G . The relationship between SpS(G ) and Sp(G) is stud...

We use the line digraph construction to associate an orthogonal matrix with each graph. From this orthogonal matrix, we derive two further matrices. The spectrum of each of these three matrices is considered as a graph invariant. For the first two cases, we compute the spectrum explicitly and show that it is determined by the spectrum of the adjacency matrix of the original graph. We then show ...

The spectrum of a matrix M is the multiset that contains all the eigenvalues of M. If M is a matrix obtained from a graph G, then the spectrum of M is also called the graph spectrum of G. If two graphs has the same spectrum, then they are cospectral (or isospectral) graphs. In this paper, we compare four spectra of matrices to examine their accuracy in protein structural comparison. These four ...

the noncommuting graph $nabla (g)$ of a group $g$ is asimple graph whose vertex set is the set of noncentral elements of$g$ and the edges of which are the ones connecting twononcommuting elements. we determine here, up to isomorphism, thestructure of any finite nonabeilan group $g$ whose noncommutinggraph is a split graph, that is, a graph whose vertex set can bepartitioned into two sets such t...

In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

let $g$ be an $(n,m)$-graph. we say that $g$ has property $(ast)$if for every pair of its adjacent vertices $x$ and $y$, thereexists a vertex $z$, such that $z$ is not adjacentto either $x$ or $y$. if the graph $g$ has property $(ast)$, thenits complement $overline g$ is connected, has diameter 2, and itswiener index is equal to $binom{n}{2}+m$, i.e., the wiener indexis insensitive of any other...

let $d$ be a digraph with skew-adjacency matrix $s(d)$‎. ‎the skew‎ ‎energy of $d$ is defined as the sum of the norms of all‎ ‎eigenvalues of $s(d)$‎. ‎two digraphs are said to be skew‎ ‎equienergetic if their skew energies are equal‎. ‎we establish an‎ ‎expression for the characteristic polynomial of the skew‎ ‎adjacency matrix of the join of two digraphs‎, ‎and for the‎ ‎respective skew energ...

‎in this paper we introduce mixed unitary cayley graph $m_{n}$‎ ‎$(n>1)$ and compute its eigenvalues‎. ‎we also compute the energy of‎ ‎$m_{n}$ for some $n$‎.