10079260
The sum number and integral sum number of complete bipartite graphs
Let N denote the set of positive integers. The sum graph G + (S) of a 1nite subset S of N is the graph (S; E) with vertex set S and edge set E such that for u; v ∈ S; uv ∈ E if and only if u + v ∈ S. A graph G is called a sum graph if it is isomorphic to the sum graph G + (S) of some 1nite subset S of N . The sum number � (G) of a graph G is de1ned as the smallest nonnegative integer m for which G ∪ mK1 is a sum graph. Let Z be the set of all integers. By extending the set N to Z in the above de1nitions of sum graphs and sum numbers, Harary [3] introduced the corresponding notions of integral sum graphs and integral sum number of a graph. In this paper, we evaluate the value of the sum number and integral sum number of the complete bipartite graph Kr; s. While the former one corrects the result given in [4], the latter settles completely a problem proposed in [3]. c � 2001 Elsevier Science B.V. All rights reserved.
207130271
Frobenius maps
A graph is called Frobenius if it is a connected orbital regular graph of a Frobenius group. A Frobenius map is a regular Cayley map whose underlying graph is Frobenius. In this paper, we show that almost all low-rank Frobenius graphs admit regular embeddings and enumerate non-isomorphic Frobenius maps for a given Frobenius graph. For some Frobenius groups, we classify all Frobenius maps derived from these groups. As a result, we construct some Frobenius maps with trivial exponent groups as a partial answer of a question raised by Nedela and Skoviera (Exponents of orientable maps, Proc. London Math. Soc. 75(3) (1997) 1-31).
13312657
Feedback vertex sets in star graphs
In a graph G = (V, E), a subset F ⊂ V(G) is a feedback vertex set of G if the subgraph induced by V(G) \ F is acyclic. In this paper, we propose an algorithm for finding a small feedback vertex set of a star graph. Indeed, our algorithm can derive an upper bound to the size of the feedback vertex set for star graphs. Also by applying the properties of regular graphs, a lower bound can easily be achieved for star graphs.
215142
A Study of Internet Packet Reordering
Packet reordering is a well-known phenomenon that the order of packets is inverted in the Internet. Previous studies indicates reordering can affect the performance of both the network and the packets receiver. Nevertheless, they get different results about the prevalence of reordering in the Internet. In this paper, we firstly present a methodology for single-point reordering measurement at a TCP receiver, including the algorithm and its implementation. Then we show the results of our three-week observation of reordering from a set of 10,647 Internet Web sites in China. In addition, we discuss a method to distinguish reordering and loss by making use of the distribution of their time lag and packet lag. Finally, we study the pertinence of sites experiencing reordering according to the network topology and propose a novel and relatively reliable approach to infer reorder-generating spots in the Internet.
7775956
Mining Invariants in Biological Sequences
7795893
Region-based memory management in cyclone
Cyclone is a type-safe programming language derived from C. The primary design goal of Cyclone is to let programmers control data representation and memory management without sacrificing type-safety. In this paper, we focus on the region-based memory management of Cyclone and its static typing discipline. The design incorporates several advancements, including support for region subtyping and a coherent integration with stack allocation and a garbage collector. To support separate compilation, Cyclone requires programmers to write some explicit region annotations, but a combination of default annotations, local type inference, and a novel treatment of region effects reduces this burden. As a result, we integrate C idioms in a region-based framework. In our experience, porting legacy C to Cyclone has required altering about 8% of the code; of the changes, only 6% (of the 8%) were region annotations.
11378639
Efficient Zero-Knowledge Proofs for Some Practical Graph Problems
From a cryptographic aspect zero-knowledge protocols for graph isomorphisms, graph non-isomorphisms, and graph-coloring are artificial problems, that received lots of attention. Due to recent work in network security in a broadcast setting, it seems important to design efficient zero-knowledge protocols for the following graph problems: independent set problem, neighbor independent set problem, and disjoint broadcast lines problem. In this paper, we will introduce a new concept of k-independent set problem which is a generalization of independent set and neighbor independent set problems, and we will present efficient zero-knowledge protocols for these problems. In the end of the paper we will give some cryptographic applications of k-independent set. Especially, we will point out the applications to the concept of "threshold" and appropriate access structures. Note that k-independent set also has applications outside cryptography, such as biology, methodology of scientific research, ethics, etc., which are beyond the scope of this paper.