Nicholas C. K. Phillips

Totally Magic Graphs

A total labeling of a graph with v vertices and e edges is defined as a one-to-one map taking the vertices and edges onto the integers 1,2,···,v+e. Such a labeling is vertex magic if the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex, and edge magic if the sum of an edge label and the labels of the endpoints of the edge is constant. In this paper we examine graphs possessing a labeling that is simultaneously vertex magic and edge magic. Such graphs appear to be rare.

Double Arrays, Triple Arrays and Balanced Grids

Abstract.Triple arrays are a class of designs introduced by Agrawal in 1966 for two-way elimination of heterogeneity in experiments. In this paper we investigate their existence and their connection to other classes of designs, including balanced incomplete block designs and balanced grids.

Tight single-change covering designs with v = 12, k = 4

Abstract Standardised tight single-change covering designs with v = 12, k = 4 are enumerated and classified. There are 2554 of them, and these fall into 566 sets such that, within any set, the designs can be regarded as minor variants of one another. The sets pair off naturally, to give 283 classes of the designs. If any one design in a class is row-regular (or element-regular), then all the designs in the class are row-regular (or element-regular). Of the 283 classes, just 10 comprise row-regular designs; these 10 include the only one of the 283 classes that comprises element-regular designs. Representative members of the 10 row-regular classes are tabulated. Other properties of the designs are discussed. An indication is given of how each of the 10 representative row-regular designs can readily be converted into a row-regular tight single-change covering design with v = 13, k = 4.

Finding tight single-change covering designs with v =20, k =5

Abstract The discovery is reported of tight single-change covering designs (tsccds) with v =20 and k =5. All previously known tsccds had k =2,3 or 4. The computational difficulties encountered in the computer construction of the new designs are described and discussed.

The seven classes of 5×6 triple arrays

Triple arrays are considered in which 10 symbols each appear 3 times in a 5x6 arrangement of symbols. These triple arrays fall into seven isomorphism classes. The orders of the automorphism groups of the arrays in these classes are 60, 12, 12, 6, 4, 3 and 3, respectively.

Tight single-change covering designs with upsilon=12, k=4

Standardised tight single-change covering designs with upsilon = 12, k = 4 are enumerated and classified. There are 2554 of them, and these fall into 566 sets such that, within any set, the designs can be regarded as minor variants of one another. The sets pair off naturally, to give 283 classes of the designs. If any one design in a class is row-regular (or element-regular), then all the designs in the class are row-regular (or element-regular). Of the 283 classes, just 10 comprise row-regular designs; these 10 include the only one of the 283 classes that comprises element-regular designs. Representative members of the 10 row-regular classes are tabulated. Other properties of the designs are discussed. An indication is given of how each of the 10 representative row-regular designs can readily be converted into a row-regular tight single-change covering design with upsilon = 13, k = 4.

Stream driven query processing in a database

This papa descsibea a amcurrent mechanism for processing databam queries. The &tabase is assumed to be relational end the different reladom eompriaii the database may, ifneceaaary, reside on differesttcampstesa (linked m a network). During the processing of a particular query, the prmeamm for the relations involved work concurrently by stre appropriate data through the network. Ilte paper investigates the feasibility of using umeumency S@WOItiZ?d by &tta flOW cOSSStr5itItS.