On the normalized Laplacian of Möbius phenylene chain and its applications

Let denote a molecular graph of linear [n] phenylene with n hexagons and n squares, and let the Möbius phenylene chain be the graph obtained from the by identifying the opposite lateral edges in reversed way. Utilizing the decomposition theorem of the normalized Laplacian characteristic polynomial, we study the normalized Laplacian spectrum of , which consists of the eigenvalues of two symmetric matrices ℒ _R and ℒ _Q of order 3n. By investigating the relationship between the roots and coefficients of the characteristic polynomials of the two matrices above, we obtain an explicit closed-form formula of the multiplicative degree-Kirchhoff index as well as the number of spanning trees of . Furthermore, we determine the limited value for the quotient of the multiplicative degree-Kirchhoff index and the Gutman index of .     

On the balanced domination of graphs

Czechoslovak Mathematical Journal - Let G = (VG,EG) be a graph and let NG[υ] denote the closed neighbourhood of a vertex υ in G. A function f: VG ? {?1,0,1} is said to be a...     

Structure,modification, and commercialization of high nickel ternary material (LiNi0.8Co0.1Mn0.1O2 and LiNi0.8Co0.15Al0.05O2) for lithium ion batteries

Journal of Solid State Electrochemistry - LiNi0.8Co0.1Mn0.1O2 (NCM811), as one of the most promising cathode materials for lithium ion batteries, has gained a huge market with its obvious...     

Sums of Powers of the Degrees of Graphs with k Cut Edges

For a graph G with k cut edges and a real number say ??, we consider the sum, denoted by ${R_{\alpha}^{0}(G)}$ , of the ??th powers of the degrees of the vertices of G. This sum is also called the zeroth-order general Randi? index of the (molecular) graph G. We present some sharp bounds on this sum according to ?? in different intervals.     

Integral and distance integral Cayley graphs over generalized dihedral groups

Journal of Algebraic Combinatorics - A graph is said to be integral (resp. distance integral) if all the eigenvalues of its adjacency matrix (resp. distance matrix) are integers. Let H be a finite...     

斜入射脉冲X射线产生电流实验

 针对斜入射脉冲X射线与金属的几种可能相互作用机制,设计了实验布局,测量了斜入射X射线在金属靶上产生的脉冲电流,建立了相应的理论模型。结果显示,当X射线入射强度低于10⁵ W/cm²时,以光电效应为主,高于此值时,以热电效应为主导。这表明,X射线加载强度较弱时,电子表现出个体行为,而增大X射线入射强度,电子表现出弱关联集体行为。由此可以预测,超强X射线辐照下,金属表面将出现宏观尺度的电荷密度调制,在退激发过程中,这种调制状态可能以较高的效率辐射定向的微波电磁脉冲。