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An Extension of the Rényi Formula

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Journal of Mathematical Research with Applications 2016年第3期36卷 265-271页

作者： Yufei HUANG bolian liu Department of Mathematics Teaching Guangzhou Civil Aviation College College of Mathematical Science South China Normal University

In this paper, as a natural extension of the Rényi formula which counts labeled connected unicyclic graphs, we present a formula for the number of labeled（k + 1）-uniform（p, q）-unicycles as follows:U（k+1）p, q={p... 详细信息

关键词： Labeled hypergraph (p,q)-unicycles (k + 1)-uniform Rényi formula

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非正则图的谱半径

数学物理学报（A辑） 2009年第2期29卷 233-238页

作者：柳柏濂华南师范大学数学科学学院广州510631

讨论了由***提出的给定顶点数n和最大度△的非正则图的谱半径的上界,并给出了一些新的由△表示的谱半径的界.

关键词：图最大度最大特征值谱半径.

Estimates on the Number of Edges for Network with Given Wide Diameter

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运筹学学报(中英文) 1998年第2期2卷 18-24页

作者： bolian liu BO ZHOU (Department of Mithematics, South China Normal University, Guangzhou 510631, P. R. China) 华南师范大学数学系广东广州

Wide diameter is a newly introduced parameter to measure the reliability and fault tolerance of networks. We provide lower estimates on the number of edges for k-connected network with given k-wide diameter and maximu... 详细信息

关键词： Wide Estimates on the Number of Edges for Network with Given Wide Diameter

The counting series for (k+1)-uniform linear acyclic hypergraphs

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Chinese Science Bulletin 2001年第3期46卷 197-200页

作者： SHAN Zhilong & liu bolian Department of Mathematics, South China Normal University, Guangzhou 510631, China Department of Computer Science, Guandong Polytechnical Normal University, Guangzhou 510633, China Department of Mathematics South China Normal University Guangzhou China Department of Computer Science Guandong Polytechnical Normal University Guangzhou China

The explicit formula for (k+l)-uniform linear acyclic hypergraphs and the counting series for unlabeled (k +1)-uniform linear acyclic hypergraphs are obtained.

关键词： hypergraph linear hypergraph hypertree bipartite tree Polya’s Enumeration Theorem.

ON A CONJECTURE OF HARMONIOUS GRAPH

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Systems Science and Mathematical Sciences 1989年第4期2卷 325-328页

作者：柳柏濂张显坤 South China Normal University GuangzhouChina

Let the coronas Cn⊙K1 be the polygons with one additional end-point for *** Grace conjectured that Cn⊙K1 are harmonious for n *** this paper,aproof of his conjecture is given.

关键词： Harmonious graph Sequential graph labeling coronas conjecture

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(m,n)树的几个判定定理

数学杂志 1989年第1期9卷 29-32页

作者：柳柏濂华南师范大学

(m,n)树是图论中树的概念在n维复形上的推广。关于n维复形和它的(m,n)回路,(m,n)连通,(m,n)简单,纯n维复形,(m,n)树等概念见文献[3],[4]。用a_k(K)表复形K中的k维单形个数。

关键词： (M,N)树判定定理图论几维复形

ENUMERATION OF ORIENTED TREES AND FREE TREES WITH A GIVEN NUMBER OF LEAVES

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Chinese Science Bulletin 1988年第19期33卷 1577-1581页

作者：柳柏濂 South China Normal University Guangzhou

D. E. Knuth has widely discussed some combinatorial properties and the application in computer science on binary trees, ordered trees, oriented trees and free trees, and given some formulas for the number of all the above structurally different trees with n nodes. Recently Wang Zhenyu gave formulas of the total leaf number for the preceding trees. Classifying these results carefully, Wang

关键词： enumeration oriented tree free tree