Merging the A- and Q-spectral theories

Applicable Analysis and Discrete Mathematics

article

Vladimir Nikiforov¹ 

[1] Department of Mathematical Sciences, University of Memphis

关键词: spectral Turan theorem;    spectral extremal problems;    signless Laplacian;    adjacency matrix;    Spectral radius;   

DOI  :  10.2298/AADM1701081N

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

Let G be a graph with adjacency matrix A (G), and let D (G) be the diagonalmatrix of the degrees of G. The signless Laplacian Q (G) of G is defined asQ (G) := A (G) + D (G). Cvetkovi´c called the study of the adjacency matrixthe A-spectral theory, and the study of the signless Laplacian–the Q-spectraltheory. To track the gradual change of A (G) into Q (G), in this paper itis suggested to study the convex linear combinations Aα (G) of A (G) andD (G) defined byAα (G) := αD (G) + (1 − α) A (G) , 0 ≤ α ≤ 1.This study sheds new light on A (G) and Q (G), and yields, in particular, anovel spectral Tur´an theorem. A number of open problems are discussed.

【 授权许可】

Unknown