Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897728 | Linear Algebra and its Applications | 2018 | 7 Pages |
Abstract
Let G be a finite undirected graph without loops and multiple edges. By η,Î and n we respectively denote the nullity, the maximum vertex degree and the order of G. In [10], it was proved that ηâ¤nâ2ânâ1Îâ when G is a tree. This result was generalized to a bipartite graph by [25]. For a reduced bipartite graph G, the above inequality was improved to nâ2â2ln2Î by [27]. However, the problem of bounding the nullity of an arbitrary graph G in terms of n and Î is left open for more than ten years. In this article, we aim to solve such a left problem. We prove that ηâ¤Îâ1În for an arbitrary graph G with order n and maximum degree Î, and the equality holds if and only if G is the disjoint union of some copies of KÎ,Î.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Qi Zhou, Dein Wong, Dongqin Sun,