Abstract
Motivated by progresses on study of eigenvalue sum in adjacency matrix and Laplacian matrix, in this paper, we focus on the sum of the k largest distance eigenvalues of graphs. Denote by Sk(D(G))=λ1(D(G))+⋯+λk(D(G)) the sum of the k largest distance eigenvalues of G. We initially determine the extremal graph attaining the minimum Sk(D(G)) among all threshold graphs except for complete graphs. Besides, we prove that the complete r-partite graph attains the minimum Sk(D(G)) among all graphs with chromatic number χ(G)=r and we also give the lower bounds on Sk(D(G)) when G is Kr+1-free, which are extensions of previous results from Lin (2019) and Lu & Lu (2022), respectively.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
