More on graphs with just three distinct eigenvalues

Applicable Analysis and Discrete Mathematics

article

Peter Rowlinson¹ 

[1] Mathematics and Statistics Group, Institute of Computing Science and Mathematics, University of Stirling Scotland FK9 4LA United Kingdom

关键词: Quasi-symmetric design;    minimum degree;    Strongly regular graph;    Symmetric design;    main eigenvalue;   

DOI  :  10.2298/AADM161111033R

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 connected non-regular non-bipartite graph whose adjacency matrix has spectrum ρ, µ(k), λ(l), where k, l ∈ IN and ρ > µ > λ. We show thatif µ is non-main then δ(G) ≥ 1 + µ − λµ, with equality if and only if G is ofone of three types, derived from a strongly regular graph, a symmetric designor a quasi-symmetric design (with appropriate parameters in each case).

【 授权许可】

Unknown