학술논문
Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions
Document Type
Original Paper
Source
Journal of Algebraic Combinatorics: An International Journal. 58(1):263-277
Subject
Language
English
ISSN
0925-9899
1572-9192
1572-9192
Abstract
Sharp bounds on the least eigenvalue of an arbitrary graph are presented. Necessary and sufficient (just sufficient) conditions for the lower (upper) bound to be attained are deduced using edge clique partitions. As an application, we prove that the least eigenvalue of the n-Queens graph Q(n)-4n≥4(n-3)2 is equal to Q(n)-4n≥4(n-3)2 for every Q(n)-4n≥4(n-3)2 and it is also proven that the multiplicity of this eigenvalue is Q(n)-4n≥4(n-3)2. Finally, edge clique partitions of additional infinite families of connected graphs and their relations with the least eigenvalues are presented.