Related papers: Asymptotic energy of graphs
A signed graph $\Gamma(G)$ is a graph with a sign attached to each of its edges, where $G$ is the underlying graph of $\Gamma(G)$. The energy of a signed graph $\Gamma(G)$ is the sum of the absolute values of the eigenvalues of the…
The energy $E(G)$ of a graph $G$ is defined as the sum of the absolute values of its eigenvalues. A graph $G$ of order $n$ is said to be hypoenergetic if $E(G)<n$. Majstorovi\'{c} et al. conjectured that complete bipartite graph $K_{2,3}$…
Let $G$ be a graph with the vertex set $ \lbrace v_1,\ldots,v_n \rbrace$. The Seidel matrix of $G$ is an $n\times n$ matrix whose diagonal entries are zero, $ij$-th entry is $-1$ if $ v_{i} $ and $ v_{j} $ are adjacent and otherwise is $ 1…
Asymptotic freedom is a feature of quantum chromodynamics that guarantees its well-posedeness. We derive an analog of asymptotic freedom enabling unconditional stability of lattice Boltzmann simulation of hydrodynamics. For the lattice…
The energy $E(G)$ of a graph $G$ is defined as the sum of the absolute values of its eigenvalues. Let $S_2$ be the star of order 2 (or $K_2$) and $Q$ be the graph obtained from $S_2$ by attaching two pendent edges to each of the end…
Statistical physics models with hard constraints, such as the discrete hard-core gas model (random independent sets in a graph), are inherently combinatorial and present the discrete mathematician with a relatively comfortable setting for…
The extended adjacency matrix of a graph with $n$ vertices is a real symmetric matrix of order $n\times n$ whose $(i,j)$-th entry is the average of the ratio of the degree of the vertex $i$ to that of the vertex $j$ and its reciprocal when…
We discuss the simulation of the low-energy effective field theory (EFT) for graphene in the presence of an external magnetic field. Our fully nonperturbative calculation uses methods of lattice gauge theory to study the theory using a…
For a simple connected graph $G$ of order $n$ having distance Laplacian eigenvalues $ \rho^{L}_{1}\geq \rho^{L}_{2}\geq \cdots \geq \rho^{L}_{n}$, the distance Laplacian energy $DLE(G)$ is defined as…
Suppose G is an n-vertex simple graph with vertex set {v1,..., vn} and d(i), i = 1,..., n, is the degree of vertex vi in G. The ISI matrix S(G) = [sij] of G is a square matrix of order n and is defined by sij = d(i)d(j)/d(i)+d(j) if the…
Let G be a simple graph of order $n$ and $\mu_1,\mu_2,\ldots,\mu_n$ the roots of its matching polynomial. The matching energy of $G$ is defined as the sum $\sum_{i=1}^n|\mu_i|$. Let $K_{n-1,1}^k$ be the graph obtained from $K_1\cup K_{n-1}$…
The asymptotic form of the wave functions describing a freely expanding Lieb-Liniger gas is derived by using a Fermi-Bose transformation for time-dependent states, and the stationary phase approximation. We find that asymptotically the wave…
In this article we consider a graphene sheet that is folded in various compact geometries with arbitrary topology described by a certain genus, $g$. While the Hamiltonian of these systems is defined on a lattice one can take the continuous…
We define various notions of energy of a set of vertices in a graph, which generalize two of the most widely studied graphical indices: the Wiener index and the Harary index. We provide a new proof of a result due to Douthett and Krantz,…
The low energy electronic spectra of rotationally faulted graphene bilayers are studied using a long wavelength theory applicable to general commensurate fault angles. Lattice commensuration requires low energy electronic coherence across a…
We present a lattice Boltzmann algorithm based on an underlying free energy that allows the simulation of the dynamics of a multicomponent system with an arbitrary number of components. The thermodynamic properties, such as the chemical…
In this work, we investigate energy bands in a three dimensional simple cubic lattice of contact potential. The energy bands in the first Brillouin Zone are obtained with Ewald's summation method. In comparison with single point potential,…
The enhanced power graph of a finite group $G$, denoted by $\mathcal{P}_E(G)$, is the simple undirected graph whose vertex set is $G$ and two distinct vertices $x, y$ are adjacent if $x, y \in \langle z \rangle$ for some $z \in G$. In this…
We consider the linear damped wave equation on finite metric graphs and analyse its spectral properties with an emphasis on the asymptotic behaviour of eigenvalues. In the case of equilateral graphs and standard coupling conditions we show…
We consider asymptotics of the ground state energy of heavy atoms and molecules in the self-generatedl magnetic field. Namely, we consider $$H=((D-A)\cdot\boldsymbol{\sigma})^2-V$$ with $$V=\sum_{1\le m\le M} \frac{Z_m}{|x-y_m|}$$ and a…