具有三个或四个不同a α-特征值的二阶分裂图的完全刻画

IF 0.7 4区数学 Q2 MATHEMATICS

Rocky Mountain Journal of Mathematics Pub Date : 2023-10-01 DOI:10.1216/rmj.2023.53.1571

Wanting Sun, Shuchao Li, Xuechao Li

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引用次数: 0

摘要

如果一个图的顶点集可以划分为团和独立集，那么这个图就是分裂的。如果分割图的每个顶点度数都等于x或y，则分割图是(x,y)双度的。每个连通的分割图的直径最多为3。2017年，Nikiforov提出了a α-矩阵，它是图g的邻接矩阵和顶点度对角矩阵的凸组合。众所周知，一个直径为l的连通图至少包含l+1个不同的a α-特征值。如果一个图的直径为l，并且恰好有l+1个不同的Aα特征值，那么我们就说这个图相对于它的Aα-矩阵是lα-极值。本文利用分割图与组合设计的关联，给出了连通的2α-极值。对3α-极值双次分裂图进行了分类。此外，所有直径为2且具有4个不同的a α-特征值的连通的二次分裂图都被识别出来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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COMPLETE CHARACTERIZATION OF THE BIDEGREED SPLIT GRAPHS WITH THREE OR FOUR DISTINCT Aα-EIGENVALUES

A graph is split if its vertex set can be partitioned into a clique and an independent set. A split graph is (x,y)-bidegreed if each of its vertex degrees is equal to either x or y. Each connected split graph is of diameter at most 3. In 2017, Nikiforov proposed the Aα-matrix, which is the convex combination of the adjacency matrix and the diagonal matrix of vertex degrees of the graph G. It is well-known that a connected graph of diameter l contains at least l+1 distinct Aα-eigenvalues. A graph is said to be lα-extremal with respect to its Aα-matrix if the graph is of diameter l having exactly l+1 distinct Aα-eigenvalues. In this paper, using the association of split graphs with combinatorial designs, the connected 2α-extremal (resp. 3α-extremal) bidegreed split graphs are classified. Furthermore, all connected bidegreed split graphs of diameter 2 having just 4 distinct Aα-eigenvalues are identified.

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来源期刊

Rocky Mountain Journal of Mathematics 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

7.5 months

期刊介绍： Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles. The Rocky Mountain Journal of Mathematics endeavors to publish significant research papers and substantial expository/survey papers in a broad range of theoretical and applied areas of mathematics. For this reason the editorial board is broadly based and submissions are accepted in most areas of mathematics. In addition, the journal publishes specialized conference proceedings.