Abstract A dominating set in a graph G is a set of vertices D such that every vertex of G is either in D or is adjacent some vertex of D. The domination number Γ(G) of G is the minimum cardinality of any dominating set. A graph is vertex domination‐critical if the removal of any vertex decreases its domination number. This paper gives examples and properties of vertex domination‐critical graphs, presents a method of constructing them, and poses some open questions. In the process several results for arbitrary graphs are presented.

Many heuristics polynomial time algorithms exist to colour the vertices of connected undirected graphs having no loops or multiple edges. Associated with each such algorithm are graphs for which the number of colours required in the colouring produced by the algorithm is significantly greater than the minimum that are necessary. Thus it is desirable to have available a range of such algorithms. One, based on a theorem of Zykov, is described here. It has performed well on most graphs to which it has been applied, including some on which other algorithms fail. However it has its own ‘bad’ graphs, and one such family is listed.

Thin paper describes an IBM 704 program which simulates mall processing systems within any United States Post Office.Such systems can be represented by a connection of basic processing operations, of which there are only four different types.Any demred connection is possible, and therefore any size postal system can be simulated.The basic processing calculations are given and the program flow chart is briefly discussed.Some of the applications and results are indicated *

Properties of binary counters which have feedback connections are discussed. Various methods of determining the cyclic period have been reported, as well as techniques for synthesizing feedback connections to obtain a specific period. This paper presents a somewhat different approach to the period determination. It also includes a discussion of a simple method for determining the numerical values eliminated from the normal counting sequence by feedback connections. Several illustrative examples are given.

Most computer in operation today have supplementary programs which do automatic coding or program assembling. These programs either translate, automatically code, or interpret pseudo instructions which in themselves may cause the enaction of hundreds of actual machine instructions. The outstanding feature of such routines is that programming time and effort is cut to a minimum. This paper deals generally with translation and interpretive schemes, and specifically with a suitable translation routing for use with the DEUCE computer. The translation program is called SODA, or Symbolic Optimum Deuce Assembly Program. Two examples of SODA use are included in the appendix.