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  2. Jul 17, 2015 · I use empty graph to mean a graph without edges, and therefore a nonempty graph would be a graph with at least one edge. According to both wikipedia.com and wikibooks.com, a trivial graph is a graph with 1 vertex and 0 edges.

  3. The graph Gis non-trivial if it contains at least one edge, i.e., E 6= ;. non-trivial Equivalently, Gis non-trivial if Gis not an empty graph. The order of G, denoted by jGj, is the number of vertices of G, i.e., jGj= jVj. order, jGj The size of G, denoted by kGk, is the number of edges of G, i.e., kGk= jEj. size, kGk

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    • 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.
  4. Jan 2, 2017 · The trivial graph is the graph on one vertex. This graph meets the definition of connected vacuously (since an edge requires two vertices). A non-trivial connected graph is any connected graph that isn't this graph.

  5. Edges of a simple graph can be described as. . E = {{v1, v2}, {v2, v3}, {v3, v4}, Graph. . The graph G is empty if V = ∅, and is trivial if E = ∅. The cardinality of the vertex-set of a graph G is called the order of G and denoted |G|. The cardinality of the edge-set of a graph G is called the size of G and denoted kGk.

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  6. 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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  8. Example 3. For every n 2N, there is a unique graph having n vertices and no edges. In this graph no two vertices are adjacent; it is sometimes called the trivial graph of n vertices. On the other hand, there is a unique graph having n vertices, where any two distinct vertices are adjacent. This is called the complete graph on n vertices, and it

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