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	1. Some Results on Edge Coloring Problems with Constraints in Graphs
	Liu Guizhen ,Hou Jianfeng
	Mathematics 12 October 2009
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	Abstract:In this paper some new results on the acyclic-edge coloring, $f$-edge coloring, $g$-edge cover coloring, $(g, f)$-coloring and equitable edge-coloring of graphs are introduced. In particular, some new results related to the above colorings obtained by us are given. Some new problems and conjectures are presented.
	TO cite this article:Liu Guizhen ,Hou Jianfeng . Some Results on Edge Coloring Problems with Constraints in Graphs[OL].[12 October 2009] http://en.paper.edu.cn/en_releasepaper/content/35731


	2. On the asymptotic behavior of graphs determined by their generalized spectra
	wangwei,Cheng-xian Xu
	Mathematics 10 August 2009
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	Abstract:In previous papers, the authors introduced a family of graphs $mathcal{H}_n$ and gave some methods for finding graphs among this family that are determined by their generalized spectra. This paper is a continuation of our previous work. We further show that almost all graphs in $mathcal{H}_n$ are determined by their generalized spectra. This gives some evidences for the conjecture that almost all graphs are determined by their generalized spectra.
	TO cite this article:wangwei,Cheng-xian Xu. On the asymptotic behavior of graphs determined by their generalized spectra[OL].[10 August 2009] http://en.paper.edu.cn/en_releasepaper/content/34360

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	3. Energy change of Bipartite unicyclic graph with k
	chen zhiwen
	Mathematics 19 March 2009
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	Abstract:G is a (molecular)graph,its energy ,denoted by E(G),is definedto be the absolute values of all eigenvalues of adjacency matrix of G.Let ɡ2l,r,k1,k2 (k1 ≥k2≥ 0) the graph obtained by attaching k1 And k2 pendent edges to the first vertex and the r-th vertex of the cycle Cl,respectively.Wecharacterized energy change and the extremalenergy graphs in ɡ2l,r,k1,k2 (k1 ≥k2≥ 0).
	TO cite this article:chen zhiwen. Energy change of Bipartite unicyclic graph with k[OL].[19 March 2009] http://en.paper.edu.cn/en_releasepaper/content/30509


	4. On the Size of Critical Graphs with Maximum Degree Eight
	Sun Qingbo,Zhang Junping
	Mathematics 02 March 2009
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	Abstract:In the paper,we researched the dischange methods which had been applied for solving many problems of the adjacent characteristics of edge chromatic critical graphs,giving new lower bounds for the size of 8-critical graphs.Although the Vizing\
	TO cite this article:Sun Qingbo,Zhang Junping. On the Size of Critical Graphs with Maximum Degree Eight[OL].[ 2 March 2009] http://en.paper.edu.cn/en_releasepaper/content/29793


	5. The Average Degree of Critical Graphs with Maximum Degree Nine
	Sun Qingbo,Zhang Junping
	Mathematics 27 February 2009
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	Abstract:In the paper,we researched the dischange methods which had been applied for solving many problems of the adjacent characteristics of edge chromatic critical graphs,giving new lower bounds for the size of 9-critical graphs.Although the Vizing\
	TO cite this article:Sun Qingbo,Zhang Junping. The Average Degree of Critical Graphs with Maximum Degree Nine[OL].[27 February 2009] http://en.paper.edu.cn/en_releasepaper/content/29755


	6. Degree-distribution Stability of Growing Networks
	Zhentin Hou,Xiangxing Kong,Dinghua Shi,Guanrong Chen,Qinggui Zhao
	Mathematics 14 January 2009
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	Abstract:In this paper, we abstract a kind of stochastic processes from evolving processes of growing networks, this process is called growing network Markov chains. Thus the existence and the formulas of degree distribution are transformed to the corresponding problems of growing network Markov chains. First we investigate the growing network Markov chains, and obtain the condition in which the steady degree distribution exists and get its exact formulas. Then we apply it to various growing networks. With this method, we get a rigorous, exact and unified solution of the steady degree distribution for growing networks.
	TO cite this article:Zhentin Hou,Xiangxing Kong,Dinghua Shi, et al. Degree-distribution Stability of Growing Networks[OL].[14 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27766


	7. On a conjecture of He concerning the spectral reconstruction of matrices
	Wang Wei
	Mathematics 21 November 2008
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	Abstract:This paper is concerned with a recent conjecture of He [Eigenvectors and reconstruction, The Electronic Journal of Combinatorics, Vol 14 (1), 2007.] on the spectral reconstruction of matrices．　Let Ａ be 　an ｎｘｎ symmetric real matrix. Then there exits an orthogonal group Ｇ（Ａ） such that for any real symetric matrix Ｂ of order ｎ，＄＼ｐｈｉ（Ａ）＝＼ｐｈｉ（Ｂ）＄ and ＄＼ｐｈｉ（Ａ＿ｉ）＝＼ｐｈｉ（Ｂ＿ｉ）＄ iff there exists an orthogonal matrix ＄Ｕ＼ｉｎ｛Ｇ（Ａ）｝＄，such that ＄Ｂ＝Ｕ︿ＴＡＵ＄，where ＄＼ｐｈｉ（．）＄ denotes the corresponding characteristic polynomial of matrices, and ＄Ａ＿ｉ，Ｂ＿ｉ＄ are matrices obtained from ＄Ａ，Ｂ＄ by deleting the ith row and i-th column. The famous reconstruction conjecture in graph theory( also known as Kelly-Ulam’s conjecture) asserts that graphs with orders larger than 2 can be determined up to isomorphism by their vertex-deleted grapgs. The conjecture of He is a natural analogue of the reconstructin conjecture to the spectral reconstruction of matrices. This paper gives a counterexample to He\\\\\\\\\\\\\\\
	TO cite this article:Wang Wei. On a conjecture of He concerning the spectral reconstruction of matrices[OL].[21 November 2008] http://en.paper.edu.cn/en_releasepaper/content/25956


	8. The minimal spectral radius of graphs with a given independence number
	Xu Mimi,Shu Jinlong ,Zhai Mingqing
	Mathematics 08 October 2008
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	Abstract:The independence number $alpha(G)$ of $G$ is defined as the maximum cardinality of a set of pairwise non-adjacent vertices which is called an independent set. In this paper, we characterize the graphs on$n$ vertices having the minimal spectral radius with independence number $alpha in{1,2,lceil frac{n}{2}rceil,lceilfrac{n}{2}rceil+1,n-3,n-2,n-1}$.
	TO cite this article:Xu Mimi,Shu Jinlong ,Zhai Mingqing . The minimal spectral radius of graphs with a given independence number[OL].[ 8 October 2008] http://en.paper.edu.cn/en_releasepaper/content/24624


	9. Hosoya polynomials of TUC_4C_8(R) nanotubes
	Jianfu Chen,Shoujun Xu,Heping Zhang
	Mathematics 24 March 2008
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	Abstract:For a connected graph G, the Hosoya polynomial ( or called Wiener polynomial) of G is a distance-based polynomial in the variable x: the coefficient of the term x^k is the number of pairs of vertices at distance k. In this paper, we obtain analytical expressions for Hosoya polynomials of TUC_4C_8(R) nanotubes, graphs covering nanotubes by alternating rhombs C_4 and octagons C_8. Furthermore, the formulae of the Wiener index and the hyper-Wiener index are obtained.
	TO cite this article:Jianfu Chen,Shoujun Xu,Heping Zhang. Hosoya polynomials of TUC_4C_8(R) nanotubes[OL].[24 March 2008] http://en.paper.edu.cn/en_releasepaper/content/19619


	10. Cutsets and Hamiltonian cycles of Johnson graphs
	Wantao Ning,Qiuli Li,Heping Zhang
	Mathematics 18 March 2008
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	Abstract:For a vertex $v$ in a graph $G$, a local cut at $v$ is a set of size $d(v)$ consisting of the vertex $x$ or the edge $vx$ for each $xin N(v)$. A diameter-increasing set in a graph $G$ is a set $U$ of vertices and edges such that the diameter of $G-U$ exceeds the diameter of $G$. In the present work, we first prove that every smallest generalized cut of Johnson graph $J(n,k)$ except $J(4,2)$ is a local cut. Then we show that every smallest diameter-increasing set in $J(n,k)$ except $J(n,2)$ and $J(6,3)$ is a subset of a local cut. Finally, we obtain that $J(n,k)$ has a Hamiltonian cycle for $n\\\\\\\\\\\\\\\\geq 3$.
	TO cite this article:Wantao Ning,Qiuli Li,Heping Zhang. Cutsets and Hamiltonian cycles of Johnson graphs[OL].[18 March 2008] http://en.paper.edu.cn/en_releasepaper/content/19393

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