Weiqiang Li

University of Delaware | UDel UD · Department of Mathematical Sciences

Let $G$ be a distance-regular graph of order $v$ and size $e$. In this paper, we show that the max-cut in $G$ is at most $e(1-1/g)$, where $g$ is the odd girth of $G$. This result implies that the independence number of $G$ is at most $\frac{v}{2}(1-1/g)$. We use this fact to also study the extendability of matchings in distance-regular graphs. A g...

A graph G of even order v is called t-extendable if it contains a perfect matching, t < v/2 and any matching of t edges is contained in some perfect matching. The extendability of G is the maximum t such that G is t-extendable. In this paper, we study the extendability properties of strongly regular graphs. We improve previous results and classify...

Let $q=p^e$, where $p$ is a prime and $e\geq 1$ is an integer. For $m\geq 1$, let $P$ and $L$ be two copies of the $(m+1)$-dimensional vector spaces over the finite field $\mathbb{F}_q$. Consider the bipartite graph $W_m(q)$ with partite sets $P$ and $L$ defined as follows: a point $(p)=(p_1,p_2,\ldots,p_{m+1})\in P$ is adjacent to a line $[l]=[l_1...

In this paper, we show that the minimum number of vertices whose removal disconnects a connected strongly regular graph into non-singleton components, equals the size of the neighborhood of an edge for many graphs. These include blocks graphs of Steiner $2$-designs, many Latin square graphs and strongly regular graphs whose intersection parameters...