Fractional decompositions and the smallest-eigenvalue separation
Combinatorics
2019-07-22 v1
Abstract
A new method is introduced for bounding the separation between the value of and the smallest eigenvalue of a non-bipartite -regular graph. The method is based on fractional decompositions of graphs. As a consequence we obtain a very short proof of a generalization and strengthening of a recent result of Qiao, Jing, and Koolen [Non-bipartite distance-regular graphs with a small smallest eigenvalue, Electronic J. Combin. 26(2) (2019), P2.41] about the smallest eigenvalue of non-bipartite distance-regular graphs.
Keywords
Cite
@article{arxiv.1907.08447,
title = {Fractional decompositions and the smallest-eigenvalue separation},
author = {Fiachra Knox and Bojan Mohar},
journal= {arXiv preprint arXiv:1907.08447},
year = {2019}
}