13651032
Bipartite density of cubic graphs
We first obtain the exact value for bipartite density of a cubic line graph on n vertices. Then we give an upper bound for the bipartite density of cubic graphs in terms of the smallest eigenvalue of the adjacency matrix. In addition, we characterize, except in the case n = 20, those graphs for which the upper bound is obtained.
5632028
On the Laplacian Spectra of Graphs
We first establish the relationship between the largest eigenvalue of the Laplacian matrix of a graph and its bipartite density. Then we present lower and upper bounds for the largest Laplacian eigenvalue of a graph in terms of its largest degree and diameter.
15047459
Disjoint Triangles of a Cubic Line Graph
Abstract.In this paper, we prove that a cubic line graph G on n vertices rather than the complete graph K4 has vertex-disjoint triangles and the vertex independence number . Moreover, the equitable chromatic number, acyclic chromatic number and bipartite density of G are respectively.
2337601
Bipartite graphs with small third Laplacian eigenvalue
In this paper, all connected bipartite graphs are characterized whose third largest Laplacian eigenvalue is less than three. Moreover, the result is used to characterize all connected bipartite graphs with exactly two Laplacian eigenvalues not less than three, and all connected line graphs of bipartite graphs with the third eigenvalue of their adjacency matrices less than one.
17354053
Graphs with fourth Laplacian eigenvalue less than two
In this paper, all connected graphs with the fourth largest Laplacian eigenvalue less than two are determined, which are used to characterize all connected graphs with exactly three Laplacian eigenvalues no less than two. Moreover, we determine bipartite graphs such that the adjacency matrices of their line graphs have exactly three nonnegative eigenvalues.
9689230
Doubly stochastic matrices of trees
Abstract In this paper, we obtain sharp upper and lower bounds for the smallest entries of doubly stochastic matrices of trees and characterize all extreme graphs which attain the bounds. We also present a counterexample to Merris’ conjecture on relations between the smallest entry of the doubly stochastic matrix and the algebraic connectivity of a graph in [R. Merris, Doubly stochastic graph matrices II, Linear Multilinear Algebr. 45 (1998) 275–285].
3788531
Degree-Light-Free Graphs and Hamiltonian Cycles
Abstract. Let G and H be graphs. G is said to be degree-light H-free if G is either H-free or, for every induced subgraph K of G with K≅H, and every {u,v}⊆K, distK(u,v)=2 implies max {d(u),d(v)}≥|V(G)|/2. In this paper, we will show that every 2-connected graph with either degree-light {K1,3, P6}-free or degree-light {K1,3, Z}-free is hamiltonian (with three exceptional graphs), where P6 is a path of order 6 and Z is obtained from P6 by adding an edge between the first and the third vertex of P6 (see Figure 1).
13613044
Low-Cost and Reliable Mutual Anonymity Protocols in Peer-to-Peer Networks
We present several protocols to achieve mutual communication anonymity between an information requester and a provider in a P2P information-sharing environment, such that neither the requester nor the provider can identify each other, and no other peers can identify the two communicating parties with certainty. Most existing solutions achieve mutual anonymity in pure P2P systems without any trusted central controls. Compared with two such representative ones, our protocols improve efficiency in two different ways. First, utilizing trusted third parties and aiming at both reliability and low-cost, we propose a group of mutual anonymity protocols. We show that with some limited central support, our protocols can accomplish the goals of anonymity, efficiency, and reliability. Second, we propose a mutual anonymity protocol which relies solely on self-organizations among peers without any trusted central controls. In this protocol, the returning path can be shorter than the requesting path. This protocol does not need to broadcast the requested file back to the requester so that the bandwidth is saved and efficiency is improved. In addition, this protocol does not need special nodes to keep indices of sharing files, thus eliminating the index maintenance overhead and the potential for inconsistency between index records and peer file contents. We have evaluated our techniques in a browser-sharing environment. We show that the average increase in response time caused by our protocols is negligible, and these protocols show advantages over existing protocols in a P2P system.
205875547
The hamiltonicity of bipartite graphs involving neighborhood unions
Let G = (X,Y) be a 2-connected balanced bipartite graph with |X| = |Y| = n. In this paper, we prove that if |N(x1) ∪ N(x2)| + |N(y1) ∪ N(y2)| ≥ n+2 for any {x1, x2} ⊆ X and {y1, y2} ⊆ Y, then G is hamiltonian except when G is a special graph on 8 or on 12 vertices.
14218778
Reconstruction of DNA sequencing by hybridization
MOTIVATION
It is widely recognized that the hybridization process is prone to errors and that the future of DNA sequencing by hybridization is predicated on the ability to successfully cope with such errors. However, the occurrence of hybridization errors results in the computational difficulty of the reconstruction of DNA sequencing by hybridization. The reconstruction problem of DNA sequencing by hybridization with errors is a strongly NP-hard problem. So far the problem has not been solved well.


RESULTS
In this paper, a new approach is presented to solve the reconstruction problem of DNA sequencing by hybridization, which realizes the computational part of the SBH experiment. The proposed algorithm accepts both the negative and positive errors. The computational experiments show that the algorithm behaves satisfactorily, especially for the case with k-tuple repetitions and positive errors.
2953976
A performance study of monitoring and information services for distributed systems
Monitoring and information services form a key component of a distributed system, or Grid. A quantitative study of such services can aid in understanding the performance limitations, advise in the deployment of the monitoring system, and help evaluate future development work. To this end, we study the performance of three monitoring and information services for distributed systems: the Globus Toolkit/spl reg/ Monitoring and Discovery Service (MDS2), the European Data Grid Relational Grid Monitoring Architecture (R-GMA) and Hawkeye, part of the Condor project. We perform experiments to test their scalability with respect to number of users, number of resources and amount of data collected. Our study shows that each approach has different behaviors, often due to their different design goals. In the four sets of experiments we conducted to evaluate the performance of the service components under different circumstances, we found a strong advantage to caching or pre-fetching the data, as well as the need to have primary components at well-connected sites because of the high load seen by all systems.