赋权边冠图的广义谱

The generalized spectra of the weighted edge corona graphs

网络是由点集和边集构成的图形,它在现实世界中可以有效地表示许多系统.在实际生活中,许多网络本质上是赋权的,它们的边具有不同的权重.在很多情况下,网络的边权重是已知的,通常忽略权重可以更好地理解这些系统.本文中首先给出基于两个不同图的加权边冠图的定义;其次根据它们各自的特征值,确定了它们赋权边冠图的广义邻接、拉普拉斯和无符号拉普拉斯谱.最后应用这些结果,进一步研究了赋权边冠图的基尔霍夫指标和生成树的个数问题.

Many systems can be usefully represented as networks or graphs-collections of vertices joined in pairs by edges.Many networks are intrinsically weighted,with their edges of various strengths.Cases in which edge weights are known for networks abound.In general,ignoring them can help researchers understand these systems better in theory.In this paper,the definition of weighted edge corona graph based on two different graphs is given,and then we determine the generalized adjacency,Laplacian and signless Laplacian spectrum of weighted edge corona graph with two different graphs in terms of their respective corresponding eigenvalues.Next,applying these results,we obtain the Kirchhoff index and the number of spanning trees of weighted edge corona graphs.