论文标题
图的扩展能量的新边界
New bounds of extended energy of a graph
论文作者
论文摘要
具有$ n $顶点的图的扩展邻接矩阵是$ n \ times n $的真实对称矩阵，其$（i，j）$ - 输入是顶点$ i $ y $与顶点$ j $ and fors forstrocal的$ i，当$ i，j $ i，j $ ny j nyeacent and Indiacent and Indiacent and i higecent and i higacent and Indeacent and i higeacent and Indeacent and Indeacent and In相邻的平均值的平均值。扩展的邻接基质的绝对特征值的骨料称为扩展能量。 在本文中，引入了扩展顶点能的概念，并获得了扩展顶点能的某些界限。从那里开始，我们建立了涉及顺序，大小，最大和最小程度的图的扩展能量的一些新上限。我们表明，这些是一些现有界限的改进。通过直接操纵，我们还建立了更多的扩展能量的上限和下限，这些范围与现有界限更好或无与伦比。最后，发现了诺德豪斯 - 加德杜姆型的一些改进的界限。
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 $i,j$ are adjacent and zero otherwise. The aggregate of absolute eigenvalues of the extended adjacency matrix is termed the extended energy. In this paper, the concept of extended vertex energy is introduced, and some bounds of extended vertex energy are obtained. From there, we establish some new upper bounds of the extended energy of a graph involving order, size, largest, and smallest degree. We show that those are improvements of some existing bounds. Through direct manipulation, we have also established some more upper and lower bounds of extended energy, which are either better or incomparable with the existing bounds. Finally, some improved bounds of Nordhaus-Gaddum-type are found.
