So, we’ll study the theory of a path, circuit, and cycle. We’ll also have a concise explanation about walks and trails. Finally, we’ll compile the concepts in a systematic summary. 2. Graph Basics Graphs are
These ideas and Euler's theorems are important in certain applications to real-world situations such as determining delivery routes and game theory. Three of Euler's theorems that apply to graph theory are: Euler's path theorem Euler's circuit theorem (sometimes called Euler's cycle theorem) Eu...
Sneak circuit analysisBased on graph theory, this chapter introduces three sneak circuit path analysis methods by using adjacency matrix, connection matrix and switching Boolean matrix respectively, which can find all of the circuit paths existed in the power converter, and then identify the sneak ...
A Hamiltonian circuit can be found by connecting the vertices in a graph so that the route traveled starts and ends at the same vertex. All vertices must be visited once, however, not all of the edges (or lines) need to be used. What is an example of a Hamiltonian path? A Hamiltonian...
In graph theory, an Eulerian path is a path in a graph which visits every edge exactly once. Similarly, an Eulerian circuit is an Eulerian path which starts and ends on the same vertex. They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Konigsberg problem ...
4.3.6 Shortest and longest path algorithms Given a combinational circuit in which each gate has its own delay value, suppose we want to find the critical path—that is, the path with the longest delay—from an input to an output. A trivial solution is to explicitly evaluate all paths from...
Using this system, potential hazardous catastrophes (e.g., open CT) can occur when the secondary circuit of a CT is switched off [6]. Previous efforts to improve the process of obtaining logic equations for dynamic zone selection were based on graph theory [7], [8], [9], [10]. In ...
In graph theory, an Eulerian path is a path in a graph which visits every edge exactly once. Similarly, an Eulerian circuit is an Eulerian path which starts and ends on the same vertex. They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Konigsberg problem ...
Constraints (3–4) are utilized to define closed loops, ensuring that each point has precisely one path originating from it and one terminating at it concurrently. Constraint (5) is imposed to avert the emergence of small loops, guaranteeing the absence of any sub-circuit solutions. Within ...
In graph theory, an Eulerian path is a path in a graph which visits every edge exactly once. Similarly, an Eulerian circuit is an Eulerian path which starts and ends on the same vertex. They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Konigsberg problem ...