几类特殊图的广义邻接距离谱

Generalized Adjacency Distance Spectrum of Several Classes of Special Graphs

摘要: 图谱理论近年来被很多学者广泛研究，其中对广义矩阵的研究吸引了很多学者。 最近，Pasten 和Rojo 引入了一种新的广义矩阵，为邻接矩阵和距离矩阵的凸线性组合，称为广义邻接距离矩 阵。 此外，谱极值问题也是图谱理论中的一个重要课题。 一些特殊图类经常被作为极值图类来研 究，如：块无差异图，菠萝图等。本文研究了四类特殊图的广义邻接距离谱，不仅对邻接谱和距离 谱进行了推广，也对其邻接距离谱进行了推广。

Abstract: Graph theory has been widely studied by many scholars in recent years, among which the study on generalized matrix has attracted many scholars. Recently, Pasten and Rojo introduced a new generalized matrix, which is a convex linear combination of the adjacency matrix and the distance matrix, called the generalized adjacency distance matrix. In addition, extremal spectrum is also an important subject in spectrum theory. Some special graphs are often studied as extremal graphs, such as block indifference graphs, pineapple graphs, etc. In this paper, we study the generalized adjacency distance spectrum of four kinds of special graphs. We generalize not only the adjacency spectrum and distance spectrum, but also their adjacency distance spectrum.