A search procedure is given which will determine whether Hamilton paths or circuits exist in a given graph, and will find one or all of them. A combined procedure is given for both directed and undirected graphs. The search consists of creating partial paths and making deductions which determine whether each partial path is a section of any Hamilton path whatever, and which direct the extension of the partial paths.

A Search Procedure for Hamilton Paths and Circuits

In many cases, the topology of communcation systems can be abstracted and represented as graph. Graph theories and algorithms are useful in these situations. In this paper, we introduced an algorithm to enumerate all cycles in a graph. It can be applied on digraph or undirected graph. Multigraph can also be used on for this purpose. It can be used to enumerate given length cycles without enumerating all cycles. This algorithm is simple and easy to be implemented.

A new way to enumerate cycles in graph

The directional overcurrent and distance relays of a multiloop network must be set in a sequence to ensure coordination. The starting points of the sequence are called break points. An algorithm to determine the minimum number of break points is presented. It can be readily implemented on a computer and forms a basic component of a computer-aided-design package for a protective system. >

Computer aided coordination of directional relays: determination of break points

A closed-loop system is represented by a weighted directed graph which exhibits all couplings of the system in a very clear and simple manner. The coefficients of the characteristic polynomial of the closed-loop system may be obtained with the aid of cycle families in this graph. Based on this result, a criterion for the existence of fixed modes is derived. The multiplicities of fixed modes may also be determined graph-theoretically. The consequences of structural constraints on the output feedback pattern become evident. Decentralized feedback is discussed as a special case.

Graph-theoretic characterization of fixed modes in centralized and decentralized control

In this paper, we enumerate enumeration problems and algorithms. This survey is under construction. If you know some results not in this survey or there is anything wrong, please let me know.

Enumeration of Enumeration Algorithms.

An algorithm is presented to enumerate all circuits of a linear graph The method is suitable for computerization and does not require a large computer memory The application of the procedure to some other enumeration problems is discussed

V.G.K. Murti

Papers

Enumeration of all circuits of a graph