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	1. On the Wiener Index of Trees with Maximum Degree
	LI Jing,WEI Fuyi
	Mathematics 01 June 2013
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	Abstract:The Wiener index of a graph is the sum of distances between all unordered pairs of vertices of the graph. In this paper, the fourth and fifth smallest Wiener indices of all trees with maximum degree are determined. Moreover, partial extreme graphs which reach the above lower bounds are also given.
	TO cite this article:LI Jing,WEI Fuyi. On the Wiener Index of Trees with Maximum Degree[OL].[ 1 June 2013] http://en.paper.edu.cn/en_releasepaper/content/4546426


	2. The Utility of A Class of Economic Network
	Xu Lan,Xu Ying
	Mathematics 20 January 2013
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	Abstract:Networks play an important role in a wide range of economic phenomena. Despite this fact, standard economic theory rarely considers economic networks explicitly in its analysis. However, a major innovation in economic theory has been the use of methods stemming from graph theory to describe and study relations between economic agents in networks. This recent development has lead to a fast increase in theoretical research on economic networks. In this paper, we consider the utility of a class of economic network.
	TO cite this article:Xu Lan,Xu Ying. The Utility of A Class of Economic Network[OL].[20 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4514564

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	3. Three Types of Topological Indices of the Join of k Graphs
	LI Jing,WEI Fuyi
	Mathematics 19 January 2013
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	Abstract:The join of two vertex disjoint graphs is obtained from their union by including all edges between the vertices in one graph and the vertices in the other. This paper mainly focused on the calculation formulas of Wiener indices, hyper-Wiener indices and reverse Wiener indices of the join of k graphs based on two definitions.
	TO cite this article:LI Jing,WEI Fuyi. Three Types of Topological Indices of the Join of k Graphs[OL].[19 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4516584


	4. A Method for 4-Color Evaluation of Plain Graph
	Yu Qiu
	Mathematics 25 June 2012
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	Abstract:In this paper introduced the method of minimum immovable edges for the calculation of color function. And according to the decompose method of similarity and difference, it introduced the principle that the color number reverse never happens. Through the analysis and calculation with this method and principle, it calculated the color number of 5-cycle configuration in graph T. And then introduced an equivalent definition that the coefficient a in part A is bigger than zero, which will be the same as the reducibility of n-cycle configuration in the graph T. Finally carried out the proof that the coefficient a in part A is bigger than zero for 5-cycle configuration in graph T.
	TO cite this article:Yu Qiu. A Method for 4-Color Evaluation of Plain Graph[OL].[25 June 2012] http://en.paper.edu.cn/en_releasepaper/content/4483107


	5. List (d,1)-total labelling of graphs embedded in surfaces
	YU Yong,ZHANG Xin,LIU Guizhen
	Mathematics 29 January 2012
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	Abstract:A k-(d,1)-total labelling of a graph G is afunction c from V(G)∪E(G) to the color set {0,1,...,k} such that c(u) ≠c(v) if uv∈E(G),c(e)≠c(e') if e and e' are two adjacent edges, and \|c(u)-c(e)\|≥d if vertex u is incident to the edge e. Theminimum k such that G has a k-(d,1)-total labelling iscalled the (d,1)-total labelling number and denoted by λTd(G).Suppose that L(x) is a list of colors available to choose for eachelement x∈V(G)∪E(G). If G has a (d,1)-total labellingc such that c(x)∈L(x) for all x∈V(G)∪E(G), then wesay that c is an L-(d,1)-total labelling of G, and G is L-(d,1)-total labelable. The list (d,1)-totallabelling number, denoted by Ch T d,1(G), is the minimum k suchthat G is k-(d,1)-total labelable. In this paper, we prove that the list (d,1)-total labelling number of a graph embedded in a surface with Euler characteristic ε whose maximum degree Δ(G) is sufficiently large is at most Δ(G)+2d.
	TO cite this article:YU Yong,ZHANG Xin,LIU Guizhen. List (d,1)-total labelling of graphs embedded in surfaces[OL].[29 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4461772


	6. On the linear arboricity of 1-planar graphs
	ZHANG Xin,LIU Guizhen,WU Jianliang
	Mathematics 18 January 2012
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	Abstract:A graph is 1-planar if it can be drawn on a plane so that each edge is crossed by at most one other edge. A linear forest is a forest in which every connected component is a path. The linear arboricity $la(G)$ of a graph $G$ is the minimum number of linear forests in $G$, whose union is the set of all edges of $G$. Akiyama, Exoo and Harary conjectured that $lceilrac{Delta(G)}{2} ceilleq la(G)leq lceilrac{Delta(G)+1}{2} ceil$ for any graph $G$. In this paper, we prove that the linear arboricity of every 1-planar graph with maximum degree $Deltageq 33$ is exactly $lceilDelta/2 ceil$
	TO cite this article:ZHANG Xin,LIU Guizhen,WU Jianliang. On the linear arboricity of 1-planar graphs[OL].[18 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4461649


	7. Bounds for the crossing number of Möbius cubes
	Yan Xiaoxia,Yang Yuansheng
	Mathematics 28 October 2011
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	Abstract:Direct connect network is widely used in multiprocessors,parallel computer systems,large scale integrated circuit and other areas. Mobius cubes MQn is an important direct connect network. In this paper, we find a good drawing of MQn in the plane with computer algorithm and get better upper bounds for MQn. Also,we give lower bounds for MQn.
	TO cite this article:Yan Xiaoxia,Yang Yuansheng. Bounds for the crossing number of Möbius cubes[OL].[28 October 2011] http://en.paper.edu.cn/en_releasepaper/content/4447423


	8. The crossing number of locally twisted cubes
	Liu Bao,Yang Yuansheng
	Mathematics 13 October 2011
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	Abstract:The crossing number of a graph G is the minimum number of pairwise intersections of edges in a drawing of G. Motivated by the recent work [L. Faria, C.M.H. de Figueiredo, O. S′ykora, and I. Vrt'o, An improved upper bound on the crossing number of the hypercube, J Graph Theory 59 (2008), 145-161] which solves the upper bound conjecture on the crossing number of n-dimensional hypercube proposed by Erdfios and Guy, we give upper and lower bounds of the crossing number of locally twisted cube, which is one of variants of hypercube.
	TO cite this article:Liu Bao,Yang Yuansheng. The crossing number of locally twisted cubes[OL].[13 October 2011] http://en.paper.edu.cn/en_releasepaper/content/4445827


	9. A graph invariant and 2-factoriations of a graph
	Xie Yingtai
	Mathematics 06 June 2010
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	Abstract:A spanning subgraph of a graph G is called a [0,2]-factor of G, if for. is a union of some disjoint cycles, paths and isolate vertices, that span the graph G. It is easy to get a [0,2]-factor of G and there would be many of [0,2]-factors for a G.A characteristic number for a [0,2]-factor, which reflect the number of the paths and isolate vertices in it,is defineted. The [0,2]-factor of G is called maximum if its characteristic number is minimum, and　is called characteristic number of G.　It to be proved that characteristic number of graph is a graph invariant and a polynomial time algorithm for computing a maximum [0,2]-factor of a graph G has been given in this paper. 　A [0,2]-factor is Called a 2-factor, if its characteristic number is zero. That is,　a 2-factor is a set of some disjoint cycles, that span G.We propose a A polynomial time algorism for computing 2-factor from a [0,2]-factor,which can be got easily. 　A HAMILTON Cycle is a 2-factor, therefore a necessary condition of a HAMILTON Graph is that, the graph have a 2-factor or the characteristic number of the graph is zero. The algorism, given in this paper, make it possible to examine the condition in polynomial time.
	TO cite this article:Xie Yingtai. A graph invariant and 2-factoriations of a graph[OL].[ 6 June 2010] http://en.paper.edu.cn/en_releasepaper/content/4375381


	10. 5-incidence chromatic motif and its application
	Meng Xianyong
	Mathematics 26 March 2010
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	Abstract:Incidence coloring of a graph G is a mapping from the set of incidences to a color-set C such that adjacent incidences of G are assigned distinct colors. The incidence coloring conjecture (ICC) states that the incidence coloring number of every graph is at most maximum degree summing 2, .Although ICC is false in general, but it has been showed for any graph with maximum degree summing 2, ICC holds. It is NP-complete to determine whether a graph with maximum degree less3 is 4-incidencecolorable. In this paper, we study some graphs with incidence coloring number is 5.
	TO cite this article:Meng Xianyong . 5-incidence chromatic motif and its application[OL].[26 March 2010] http://en.paper.edu.cn/en_releasepaper/content/41208

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