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There are 23 papers published in subject: > since this site started. |
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1. $Z_3$-connectivity for power graphs | |||
LI Xiangwen | |||
Mathematics 13 June 2017 | |||
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Abstract:Let $G$ be a connected graph. For an integer $kgeq 2$, $G^k$ isdefined to be a graph obtained from $G$ by adding new edge $uv$where $2leq d(u, v)leq k$. Let $A$ be an Abelian group with$|A|geq 3$. In this note, we prove that for any connected graph$G$, $G^l$ is $Z_3$-connected if and only if $|V(G)|geq 5$ or$Gcong K_1$, where $lgeq 3$. | |||
TO cite this article:LI Xiangwen. $Z_3$-connectivity for power graphs[OL].[13 June 2017] http://en.paper.edu.cn/en_releasepaper/content/4736426 |
2. Unicyclic graphs with the fourth extremal Wiener indices | |||
YANG Yu-Jun,CAO Yu-Liang,Wang Guang-Fu | |||
Mathematics 22 March 2017 | |||
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Abstract:Unicyclic graphs with the fourth extremal Wiener indices are characterized. It is shown that among all unicyclic graphs with $ngeq 8$ vertices,$C_5(S_{n-4})$ and $C_2^{u_1,u_2}(S_3,S_{n-4})$ have the fourth minimum Wiener indices, whereas $C^{u_1,u_2}_3(P_{3},P_{n-4})$ has the fourth maximum Wiener index. | |||
TO cite this article:YANG Yu-Jun,CAO Yu-Liang,Wang Guang-Fu. Unicyclic graphs with the fourth extremal Wiener indices[OL].[22 March 2017] http://en.paper.edu.cn/en_releasepaper/content/4722647 |
3. Extremal Graphs with Maximum Edge-Neighbor-Connectivity | |||
BAI Yan-Ru, ZHANG Zhao, LIU Qing-Hai | |||
Mathematics 26 August 2015 | |||
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Abstract:An edge is subverted if the two ends of the edge aredeleted from the graph. The edge-neighbor-connectivity$lambda_{NB}(G)$ is the minimum number of edges the subversion ofwhich results in an empty, or trivial, or disconnected graph. It isknown that $lambda_{NB}(G)leqlfloor n/2 floor$, where$n=|V(G)|$. In this paper, we characterize all extremal graphs whoseedge-neighbor-connectivity reaches this upper bound: for even $n$,an extremal graph can only be the complete graph $K_n$ or thecomplete bipartite graph $K_{rac{n}{2},rac{n}{2}}$; for odd $n$,an extremal graph can only be the 5-cycle $C_5$, or $K_n-M_0$ (thecomplete graph with a matching $M_0$ removed, where $M_0$ is anarbitrary matching of $K_n$ containing $i$ edges for $iin{0,1,ldots,lfloor n/2 floor}$), or a graph $G$ spanned by a$K_{lfloor rac{n}{2} floor,lceil rac{n}{2} ceil}$ such thatthe $lfloor n/2 floor$-part is independent in $G$ and the subgraphinduced by the $lceil n/2 ceil$-part has matching number at mostone. | |||
TO cite this article:BAI Yan-Ru, ZHANG Zhao, LIU Qing-Hai. Extremal Graphs with Maximum Edge-Neighbor-Connectivity[OL].[26 August 2015] http://en.paper.edu.cn/en_releasepaper/content/4653169 |
4. Diameter variation of directed cycles and directed tori | |||
MA Xiao-Yan, Huang Xiao-Hui, ZHANG Zhao | |||
Mathematics 26 August 2015 | |||
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Abstract:In this paper, we study two parameters concerningwith the diameter variation under the addition or deletion of arcsin a digraph $G$: $D^{-0}(G)$ is the maximum number of arcs theaddition of which dose not change the diameter of $G$; $D^{+k}(G)$is the minimum number of arcs the deletion of which increases thediameter of $G$ by at least $k$. We give a formula for $D^{-0}(G)$if $G$ is vertex transitive and every vertex has a unique vertexwhich is farthest from it. As consequences, the values of $D^{-0}$for the directed cycle and the directed torus can be determined. Thevalues of $D^{+k}$ for these two digraphs are also determined. | |||
TO cite this article:MA Xiao-Yan, Huang Xiao-Hui, ZHANG Zhao. Diameter variation of directed cycles and directed tori[OL].[26 August 2015] http://en.paper.edu.cn/en_releasepaper/content/4653178 |
5. A Steepest Descent Method on Lie Groups and its Application in Localization Problem | |||
QIN Han, YING Shi-Hui | |||
Mathematics 09 January 2014 | |||
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Abstract:In this paper, through defining a universal steepest descent direction, an intrinsic iteration algorithm for optimization problem on Lie groups is proposed. Besides two global convergence theorems about the algorithm, the convergence analysis shows that the algorithm is at least linearly convergent. As an application example, the proposed algorithm is applied to the localization problem of workpiece machining. The numerical results show that the algorithm is really steepest descent and hence efficient. | |||
TO cite this article:QIN Han, YING Shi-Hui. A Steepest Descent Method on Lie Groups and its Application in Localization Problem[OL].[ 9 January 2014] http://en.paper.edu.cn/en_releasepaper/content/4581505 |
6. Primal and dual objective space algorithms for solving linear multiplicative programmes | |||
SHAO Li-zhen,Ehrgott Matthias | |||
Mathematics 15 October 2013 | |||
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Abstract:%It is known that for most of gene expression data for cancer classification, the number of samples is quite small compared to the number of genes. Therefore, feature selection is an essential pre-processing step and a challenging problem to remove the irrelevant or redundant genes before classification.Multiplicative programming (MPP) problems are global optimisation problems known to be NP-hard.In this paper, we focus on linear MPP problems. First, we improve our own objective space cut and bound algorithm for convex MPPs in the special case of linear MPPs by only solving one linear program at each iteration step instead of two as the previous version indicates. We call this algorithm ``primal objective space algorithm". Then based on the dual variant of Benson's algorithm, we propose a ``dual objective space algorithm" for solving linear MPP problems. Again the dual algorithm requires solving only one scalar linear program in each iteration step. We prove the correctness of the dual algorithm and use computational experiments to demonstrate the superiority of the new algorithms compared to existing algorithms from the literature. | |||
TO cite this article:SHAO Li-zhen,Ehrgott Matthias. Primal and dual objective space algorithms for solving linear multiplicative programmes[OL].[15 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4564266 |
7. A Proximal Method for Solving Vector Variational Inequalities | |||
CHEN Chun-Rong | |||
Mathematics 25 September 2013 | |||
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Abstract:In this paper, based on choosing at each iteration a different vectorization to the iterated matrix, a proximal-type method for solving the weak vector variational inequality problem (mbox{WVVI}) in finite-dimensional spaces is proposed. Under appropriate assumptions, it was proved that the generated subsequence converges to a solution of problem $(mbox{WVVI})$, if the problem $(mbox{WVVI})$ has strong solutions. Moreover, if the solution set of $(mbox{WVVI})$ coincides with its strong solution set, then the whole sequence converges to a strong solution of problem (mbox{WVVI}). | |||
TO cite this article:CHEN Chun-Rong. A Proximal Method for Solving Vector Variational Inequalities[OL].[25 September 2013] http://en.paper.edu.cn/en_releasepaper/content/4561636 |
8. 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 |
9. A new polynomial-time interior-point algorithms for the Cartesian $P_*(kappa)$-SCLCP | |||
WANG Guoqiang,BAI Yanqin | |||
Mathematics 20 February 2012 | |||
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Abstract:In this paper, we generalize primal-dual interior-point method, which wasstudied by Bai et al. [Y.Q. Bai, M. El Ghami and C. Roos, ewblock {A new efficient large-update primal-dual interior-point method based on a finite barrier,} ewblock {SIAM J. Optim.} 13(3), 766-782 (2003)]for linear optimization to the Cartesian P*(k)-linear complementarity problem over symmetric conesvia Euclidean Jordan algebras. The symmetry of the resulting search directionsis forced by using the Nesterov-Todd scaling scheme.Moreover, we derive the iteration-bounds that match the currently bestknown iteration-bounds for large- and small-update methods, namelyO((1+2k)√ ̄r log r log r/ε) and O((1+2k)√ ̄r log r/ε), respectively,where r denotes the rank of the associated Euclidean Jordanalgebra and $arepsilon$ the desired accuracy. | |||
TO cite this article:WANG Guoqiang,BAI Yanqin. A new polynomial-time interior-point algorithms for the Cartesian $P_*(kappa)$-SCLCP[OL].[20 February 2012] http://en.paper.edu.cn/en_releasepaper/content/4465263 |
10. 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 |
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