‎let $g$ be a graph with vertex set $v(g)$ and edge set $x(g)$ and consider the set $a={0,1}$‎. ‎a mapping $l:v(g)longrightarrow a$ is called binary vertex labeling of $g$ and $l(v)$ is called the label of the vertex $v$ under $l$‎. ‎in this paper we introduce a new kind of graph energy for the binary labeled graph‎, ‎the labeled graph energy $e_{l}(g)$‎. ‎it depends on the underlying graph $g$...

let $g=(v‎, ‎e)$ be a graph with $p$ vertices and $q$ edges‎. ‎an emph{acyclic‎ ‎graphoidal cover} of $g$ is a collection $psi$ of paths in $g$‎ ‎which are internally-disjoint and cover each edge of the graph‎ ‎exactly once‎. ‎let $f‎: ‎vrightarrow {1‎, ‎2‎, ‎ldots‎, ‎p}$ be a bijective‎ ‎labeling of the vertices of $g$‎. ‎let $uparrow!g_f$ be the‎ ‎directed graph obtained by orienting the...

in this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. some examples are provided to show the accuracy and reliability of the proposed method. it is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to t...

The missing label for basis vectors of [Formula: see text] representations corresponding to the reduction can be provided by eigenvalues scalars in enveloping algebra text]. There are only two such independent elements degrees three and four. It is shown how one degree four diagonalized using analytical Bethe ansatz.

The question of determining for which eigenvalues there exists an eigenfunction has the same number nodal domains as label associated eigenvalue (Courant-sharp property) was motivated by analysis minimal spectral partitions. In previous works, many examples have been analyzed corresponding to squares, rectangles, disks, triangles, tori, M\"obius strips,\ldots . A natural toy model further inves...

We review the Johnson–Moser rotation number and the K0-theoretical gap labelling of Bellissard for one-dimensional Schrödinger operators. We compare them with two further gap labels, one being related to the motion of Dirichlet eigenvalues, the other being a K1-theoretical gap label. We argue that the latter provides a natural generalization of the Johnson–Moser rotation number to higher dimens...

In this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to th...

A hypergraph is said to be oriented if each edge-vertex incidence has a label of +1 or −1. An called balanced there exists bipartition the vertex set such that every edge intersects one part in positively incident vertices with and other negatively edge. In this paper, we investigate balance hypergraphs induced signed by means eigenvalues associated matrices tensors provide spectral method char...

An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of +1 or −1. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian matrices of an oriented hypergraph which depend on structural parameters of the oriented hypergraph are found. An oriented hypergraph and its incidence dual are ...

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...