Showing papers on "Adjacency list published in 1970"
TL;DR: In this paper, the derived graph of a graph G has the edges of G as its vertices, with adjacency determined by the adjacencies of the edges in G, and a new characterization of derived graphs is given in terms of nine excluded subgraphs.
270 citations
TL;DR: In this paper, the connection set determined by the first row of a circulant adjacency matrix is shown to not be multiplicatively related to the connected set of an isomorphic graph.
226 citations
Book•
01 Jan 1970
TL;DR: In this article, a linear graph representation for floor plans is developed, which is the dual graph of the floor plan, and the edges correspond to adjacencies between rooms, where the vertices correspond to rooms.
Abstract: : The work presented is intended as a case study in computer-implemented design. Its purpose is to illustrate the relationship between the representation chosen for a design problem and the methods developed for solving that problem. A formal class of 'floor plan'-type design problems is defined. In these problems a set of rectangular rooms is specified, and an allowable list of dimensions is given for each room. In addition, a set of required adjacencies between rooms, or between a room and an outside wall of the building, is given. The problem is to produce a rectangular floor plan of a building that contains all of the specified rooms, and that satisfied all of the adjacency and dimension requirements. A linear graph representation for floor plans is developed. This graph is the dual graph of the floor plan, itself treated as a linear graph. Thus, the nodes of the dual graph correspond to rooms, and the edges correspond to adjacencies between rooms. The design methods are implemented in a computer program, GRAMPA, written in IPL-V. Several illustrative problems solved by GRAMPA are discussed. (Author)
24 citations