Hua Wanghttps://works.bepress.com/hua_wang/Recent works by Hua Wangen-usCopyright (c) 2019 All rights reserved.Sat, 01 Apr 2017 07:00:00 +00003600On Algorithms for Enumerating Subtrees of Hexagonal and Phenylene Chainshttps://works.bepress.com/hua_wang/128/<p>As one of the counting-based topological indices, the number of subtrees and its variations has received much attention in recent years. In this paper, using generating functions, we investigate and derive formulas for this index of hexagonal and phenylene chains. We also present graph-theoretical algorithms for enumerating subtrees of these two chains. Extremal values and graphs with respect to the subtree number among all hexagonal and phenylene chains with <em>n</em> hexagons are also determined. As an application, we briefly examine the subtree densities of these two chains.</p>
Sat, 01 Apr 2017 07:00:00 +0000https://works.bepress.com/hua_wang/128/Journal ArticlesCombinatorics of n-Colored Cyclic Compositionshttps://works.bepress.com/hua_wang/131/<p>Integer compositions and related enumeration problems have been of interests to combinatorialists and number theorists for a long time. The cyclic and colored analogues of this concept, although interesting, have not been extensively studied. We explore the combinatorics of n-colored cyclic compositions, presenting generating functions, bijections, asymptotic formulas related to the number of such compositions, and the number of parts and the number of restricted parts of certain cyclic compositions.</p>
Sun, 12 Mar 2017 08:00:00 +0000https://works.bepress.com/hua_wang/131/Selected Academic TalksRandom Graphs and L-Connectivitieshttps://works.bepress.com/hua_wang/133/<p>For an integer l ≥ 2, the l-connectivity κl(G) of a graph G is defined to be the minimum number of vertices of G whose removal produces a disconnected graph with at least l components or a graph with fewer than l vertices. The l-edge-connectivity λl(G) of a graph G is the minimum number of edges whose removal leaves a graph with at least ` components if |V (G)| ≥ l, and λl(G) = |E(G)| if |V (G)| < l. In this paper, we establish sharp threshold functions for the l-connectivity and l-edge-connectivity of random graphs, which generalize the result of Erdos and Renyi, and Stepanov. In fact, further strengthening our results, we show that in the random graph process, with high probability the hitting times of minimum degree at least k and of l-connectivity (or l-edge-connectivity) at least k(l − 1) coincide. This can be seen as a generalization of the results of Bollobas and Thomassen.</p>
Sat, 11 Mar 2017 08:00:00 +0000https://works.bepress.com/hua_wang/133/Selected Academic TalksPattern Packing: Questions and Observationshttps://works.bepress.com/hua_wang/135/<p>Pattern packing, as opposed to the well-known question of pattern avoidance, aims to include as many as possible of a prescribed pattern in a permutation of given length. In this talk we will present an overview of the study of pattern packing in permutations and its variations such as colored permutations, preferential arrangements, and circular permutations.</p>
Mon, 06 Mar 2017 08:00:00 +0000https://works.bepress.com/hua_wang/135/Selected Academic TalksParts and Subword Patterns in Compositionshttps://works.bepress.com/hua_wang/115/<p>We find relationships between subword patterns and residue classes of parts in the set of integer compositions of a given weight. In particular, we show that it is always possible to express the total number of parts in compositions of <em>n</em> that are congruent to<em> i</em> modulo <em>m</em> as a linear combination of the total number of occurrences of subword patterns of length no more than <em>m</em>. We also find an explicit formula enumerating all such parts.</p>
Sun, 01 Jan 2017 08:00:00 +0000https://works.bepress.com/hua_wang/115/Journal Articlesl-Connectivity and l-Edge-Connectivity of Random Graphshttps://works.bepress.com/hua_wang/132/<p>For an integer l ≥ 2, the l-connectivity κl(G) of a graph G is defined to be the minimum number of vertices of G whose removal produces a disconnected graph with at least l components or a graph with fewer than l vertices. The l-edge-connectivity λl(G) of a graph G is the minimum number of edges whose removal leaves a graph with at least l components if |V (G)| ≥ l, and λl(G) = |E(G)| if |V (G)| < l. In this paper, we establish sharp threshold functions for the l-connectivity and l-edge-connectivity of random graphs, which generalize the result of Erdos and Renyi, and Stepanov. In fact, further strengthening our results, we show that in the random graph process, with high probability the hitting times of minimum degree at least k and of l-connectivity (or l-edge-connectivity) at least k(l − 1) coincide. This can be seen as a generalization of the results of Bollobas and Thomassen.</p>
Fri, 14 Oct 2016 07:00:00 +0000https://works.bepress.com/hua_wang/132/Selected Academic TalksPatterns and Parts in Compositions: Enumeration and Bijectionhttps://works.bepress.com/hua_wang/134/<p>A composition of an integer n is a tuple of positive integers that sum up to n. Our study began with the empirical observation that, in the set of all compositions of n, the total number of odd parts equals the total number of runs. We explore proofs of this fact through combinatorial as well as generating function approaches. From there we show more general results relating the number of parts in a given residue class modulo m to various subword patterns among all compositions of n.</p>
Thu, 06 Oct 2016 07:00:00 +0000https://works.bepress.com/hua_wang/134/Selected Academic TalksNote on Superpatternshttps://works.bepress.com/hua_wang/123/<p>Given a set P of permutations, a P-superpattern is a permutation that contains every permutation in P as a pattern. The study of the minimum length of a superpattern has been of interest. For P being the set of all permutations of a given length, bounds on the minimum length have been improved over the years, and the minimum length is conjectured to be asymptotic with k2/e2. Similar questions have been considered for the set of layered permutations. We consider superpatterns with respect to packing colored permutations or multiple copies of permutations. Some simple but interesting observations will be presented. We also propose a few questions.</p>
Thu, 25 Aug 2016 07:00:00 +0000https://works.bepress.com/hua_wang/123/Journal ArticlesEccentricity Sum in Treeshttps://works.bepress.com/hua_wang/124/<p>The eccentricity of a vertex, eccT(v)=maxu∈TdT(v,u), was one of the first, distance-based, tree invariants studied. The total eccentricity of a tree, Ecc(T), is the sum of eccentricities of its vertices. We determine extremal values and characterize extremal tree structures for the ratios Ecc(T)/eccT(u), Ecc(T)/eccT(v), eccT(u)/eccT(v), and eccT(u)/eccT(w) where u,w are leaves of T and v is in the center of T. In addition, we determine the tree structures that minimize and maximize total eccentricity among trees with a given degree sequence.</p>
Sun, 10 Jul 2016 07:00:00 +0000https://works.bepress.com/hua_wang/124/Journal ArticlesTrees With Given Degree Sequence and the Maximum Wiener Indexhttps://works.bepress.com/hua_wang/137/<p>Wiener index is one of the most well known and studied chemical indices. The extremal problems of finding structures that maximize or minimize the Wiener index has received much attention. The question of finding trees with a given degree sequence that maximize the Wiener index turned out to be rather complicated compared with other related results. In this talk we briefly discuss various approaches and some results regarding this question.</p>
Mon, 04 Jul 2016 07:00:00 +0000https://works.bepress.com/hua_wang/137/Selected Academic Talks