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Jan 2, 2017 · A non-trivial connected graph is any connected graph that isn't this graph. A non-trivial connected component is a connected component that isn't the trivial graph, which is another way of say that it isn't an isolated point.
- Finite Graphs. A graph is said to be finite if it has a finite number of vertices and a finite number of edges. A finite graph is a graph with a finite number of vertices and edges.
- Infinite Graph: A graph is said to be infinite if it has an infinite number of vertices as well as an infinite number of edges.
- Trivial Graph: A graph is said to be trivial if a finite graph contains only one vertex and no edge. A trivial graph is a graph with only one vertex and no edges.
- Simple Graph: A simple graph is a graph that does not contain more than one edge between the pair of vertices. A simple railway track connecting different cities is an example of a simple graph.
The combinations of r and Y for which Equation 2 holds can be presented as a negative relationship between income and the real interest rate as shown in Figure 1. The downward sloping flow-equilibrium curve---normally not a straight line as here portrayed---is called the IS curve in textbooks and we will follow that naming convention here.
Introduction. These notes include major de nitions, theorems, and proofs for the graph theory course given by Prof. Maria Axenovich at KIT during the winter term 2019/20. Most of the content is based on the book \Graph Theory" by Reinhard Diestel [4]. A free version of the book is available at http://diestel-graph-theory.com. Conventions:
A graph G is bipartite if it is the trivial graph or if its vertex set can be partitioned into two independent, non-empty sets A and B. We refer to { A, B } as a bipartiton of V(G). Note: Some people require a bipartite graph to be non-trivial. Examples include any even cycle, any tree, and the graph below. Few Observations.
Feb 18, 2022 · If G G contains vertices v,v′ v, v ′ and edge e = {v,v′}, e = {v, v ′}, then v, e,v′, e, v v, e, v ′, e, v is a nontrivial cycle which is not proper. Example 16.2.1 16.2. 1: A forest of trees. The graph in Figure 16.2.1 16.2. 1 is acyclic. Each of its connected components is a tree.
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Hamiltonian Graph- If there exists a closed walk in the connected graph that visits every vertex of the graph exactly once (except starting vertex) without repeating the edges, then such a graph is called as a Hamiltonian graph. Example- Here, This graph contains a closed walk ABCDEFG that visits all the vertices (except starting vertex ...