Zhou, "Laplacian Energy of a Graph," Linear Algebra and its Applications, vol. 414, no. 1, pp. 29 - 37, 2006.Gutman I, Zhou B. Laplacian energy of a graph. Linear Algebra and its Applications. 2006;414:29-37.I. Gutman and B. Zhou, Laplacian energy of a graph, Linear Algebra ...
The Laplacian energy of a graph G as put forward by Gutman and Zhou (see [15]) is defined asLE(G)=∑i=1n|μi−2mn|. This quantity, which is an extension of graph-energy concept has found remarkable chemical applications beyond the molecular orbital theory of conjugated molecules (see ...
Let $G$ be a simple undirected $n$-vertex graph with the characteristic polynomial of its Laplacian matrix $L(G)$, $\\\det (\\\lambda I - L (G))=\\\sum_{k = 0}^n (-1)^k c_k \\\lambda^{n - k}$. Laplacian--like energy of a graph is newly proposed graph invariant...
。直观地理解,Laplacian二次型刻画了图的“能量”(energy)。E[f]E[f]的值越小,也就意味着ff更加“光滑”(smooth),即其值不会沿着边变化得太剧烈。 事实上,我们可以做进一步地等价变换:E[f]=12⋅Eu∼v[(f(u)−f(v))2]=⟨f,f⟩−Eu∼v[f(u)f(v)]=⟨f,f⟩−⟨f,Kf⟩=...
(上 接第 199 页 ) [2]I.Gutman and Bo Zhou.Laplacian energy of a graph[J]. L inea r A lgebra A pp 1.、200 5,4 14 : 2 9—3 7. [3]Y.一P.Hou.Unicyclic graphs with minimal energy [J1. Journal of Mathemat~ al C hemistry,2 00 1,29 :16 3- 16 8 . ...
直观地理解,Laplacian二次型刻画了图的“能量”(energy),这也是我们为什么用E(f)来表示它的原因。它在其它语境下,又被称为Dirichlet形式(Dirichlet form),局部方差(local variance),解析边界大小(analytic boundary size)。 2.2 性质 关于Laplacian二次型,我们有以下事实: ...
直观地理解,Laplacian二次型刻画了图的“能量”(energy),这也是我们为什么用(mathcal{E}(f))来表示它的原因。它在其它语境下,又被称为Dirichlet形式(Dirichlet form),局部方差(local variance),解析边界大小(analytic boundary size)。 2.2 性质 关于Laplacian二次型,我们有以下事实: ...
直观地理解,Laplacian二次型刻画了图的“能量”(energy),这也是我们为什么用E(f)E(f)来表示它的原因。它在其它语境下,又被称为Dirichlet形式(Dirichlet form),局部方差(local variance),解析边界大小(analytic boundary size)。2.2 性质关于Laplacian二次型,我们有以下事实:...
句子:In quantum mechanics, the Laplacian of the wave function is related to the kinetic energy of the particle. 翻译:在量子力学中,波函数的拉普拉斯算子与粒子的动能有关。 (注:以上两句中的名著《物理世界的奇迹》和《数学与物理的桥梁》及其作者均为虚构,旨在展示“laplacian”在数学和物理领域的应用。)...
Graph Laplacian spectrum (of graph) Kirchhoff index Laplacian-energy-like invariant Laplacian energy 1. Introduction Let G=(V,E) be a simple graph with vertex set V(G)={v1,v2,…,vn} and edge set E(G), where |V(G)|=n, |E(G)|=m. Let di be the degree of the vertex vi for...