We consider the model of unconditionally secure (r-round, n-channel) message transmission schemes which was introduced by Dolev et al. [1]. In this model, there are n channels between a sender and a receiver, and an infinitely powerful adversary A may corrupt (observe and forge) the messages sent through t out of n channels. The sender wishes to send a secret s to the receiver in r-round withou...

Let G = (V,E) be a graph and let S & V. The set S is a dominating set of G is every vertex of V-S is adjacent to a vertex of S. A vertex v of G is called S-perfect if \N[t~]nsi = 1 where N[v] denotes the closed neighborhood of v. The set S is defined to be a perfect neighborhood set of G if every vertex of G is S-perfect or adjacent with an S-perfect vertex. We prove that for all graphs G, O(G)...

Object oriented development is the methodology of choice for a wide range of applications but those developing critical systems have stayed with techniques with a mathematical basis. Object-Z is a formal specication language that has attempted to bring the benets of an object oriented approach to critical systems. However, it lacks an obvious route to implementation. This paper describes how Ob...

We define a diamonded odd cycle to be an odd cycle C with exactly two chords and either a) C has length five and the two chords are non-crossing; or b) C has length greater than five and has chords (x,y) and (x,z) with (y,z) an edge of C and there exists a node w not on C adjacent to y and C, but not x. In this paper, we show that given a diamonded odd cycle-free graph G, G is perfect if and on...

In 1979, two constructions for making partitionable graphs were introduced in (by Chv2 atal et al. (Ann. Discrete Math. 21 (1984) 197)). The graphs produced by the second construction are called CGPW graphs. A near-factorization (A; B) of a %nite group is roughly speaking a non-trivial factorization of G minus one element into two subsets A and B. Every CGPW graph with n vertices turns out to b...

Minimal perfect hash functions are used for memory efficient storage and fast retrieval of items from static sets. We present an infinite family of efficient and practical algorithms for generating order preserving minimal perfect hash functions. We show that almost all members of the family construct space and time optimal order preserving minimal perfect hash functions, and we identify the on...

A 1-perfect code Cn q is called Hamiltonian if its minimum distance graph G(Cn q ) contains a Hamiltonian cycle. In this paper, for all admissible lengths n ≥ 13, we construct Hamiltonian nonlinear ternary 1-perfect codes, and for all admissible lengths n ≥ 21, we construct Hamiltonian nonlinear quaternary 1-perfect codes. The existence of Hamiltonian nonlinear q-ary 1-perfect codes of length N...

In an unpublished work of Fasel–Rao–Swan the notion relative Witt group WE(R,I) is defined. this paper, we will give details construction. Then study injectivity Vaserstein symbol VR,I:Um3(R,I)/E3(R,I)→WE(R,I). We establish if R a non-singular affine algebra dimension 3 over perfect C1-field and I local complete intersection ideal R. It natural to ask whether injective for singular 3-dimensiona...

The recently announced Strong Perfect Graph Theorem states that the class of perfect graphs coincides with the class of graphs containing no induced odd cycle of length at least 5 or the complement of such a cycle. A graph in this second class is called Berge. A bull is a graph with five vertices x, a, b, c, d and five edges xa, xb, ab, ad, bc. A graph is bull-reducible if no vertex is in two b...