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Loading... Apr 21, 2024 · A trivial graph is a graph with only one vertex and no edges. It is also known as a singleton graph or a single vertex graph. A trivial graph is the simplest type of graph and is often used as a starting point for building more complex graphs.
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- Simple Graph
- Connected Graph
- Regular Graph
- Complete Graph
- Cycle Graph
- Wheel Graph
- Bipartite Graph
- Complete Bipartite Graph
- Star Graph
- Complement of A Graph
A graph with no loops and no parallel edgesis called a simple graph. 1. The maximum number of edges possible in a single graph with ‘n’ vertices is nC2 where nC2= n(n – 1)/2. 2. The number of simple graphs possible with ‘n’ vertices = 2nc2 = 2n(n-1)/2.
A graph G is said to be connected if there exists a path between every pair of vertices. There should be at least one edge for every vertex in the graph. So that we can say that it is connected to some other vertex at the other side of the edge.
A graph G is said to be regular, if all its vertices have the same degree. In a graph, if the degree of each vertex is ‘k’, then the graph is called a ‘k-regular graph’.
A simple graph with ‘n’ mutual vertices is called a complete graph and it is denoted by ‘Kn’. In the graph, a vertex should have edges with all other vertices,then it called a complete graph. In other words, if a vertex is connected to all other vertices in a graph, then it is called a complete graph.
A simple graph with ‘n’ vertices (n >= 3) and ‘n’ edges is called a cycle graph if all its edges form a cycle of length ‘n’. If the degree of each vertex in the graph is two,then it is called a Cycle Graph. Notation − Cn
A wheel graph is obtained from a cycle graph Cn-1 by adding a new vertex. That new vertex is called a Hub which is connected to all the vertices of Cn. Notation − Wn
A simple graph G = (V, E) with vertex partition V = {V1, V2} is called a bipartite graph if every edge of E joins a vertex in V1 to a vertex in V2. In general, a Bipertite graph has two sets of vertices, let us say, V1 and V2, and if an edge is drawn, it should connect any vertex in set V1 to any vertex in set V2.
A bipartite graph ‘G’, G = (V, E) with partition V = {V1, V2} is said to be a complete bipartite graph if every vertex in V1 is connected to every vertex of V2. In general, a complete bipartite graph connects each vertex from set V1 to each vertex from set V2.
A complete bipartite graph of the form K1, n-1is a star graph with n-vertices. A star graph is a complete bipartite graph if a single vertex belongs to one set and all the remaining vertices belong to the other set.
Let 'G−' be a simple graph with some vertices as that of ‘G’ and an edge {U, V} is present in 'G−', if the edge is not present in G. It means, two vertices are adjacent in 'G−'if the two vertices are not adjacent in G. If the edges that exist in graph I are absent in another graph II, and if both graph I and graph II are combined together to form a...
Aug 3, 2023 · In graph theory, a trivial graph is the simplest and most basic type of graph that exists. It consists of just one vertex (node) and no edges. This means that a trivial graph contains only a single point without any connections to other points, as there are no edges to link it to other vertices.
Aug 5, 2024 · Trivial Graph. A trivial graph is the simplest type of graph, consisting of exactly one vertex and no edges. Consider a trivial graph with one vertices: Vertex set V: {A} Edge set E: { } or ϕ; Simple Graph. A simple graph is a type of graph in which each pair of vertices is connected by at most one edge, and no vertex has an edge to itself.
In graph theory, the trivial graph is a graph which has only 1 vertex and no edge. Database theory has a concept called functional dependency , written X → Y {\displaystyle X\to Y} . The dependence X → Y {\displaystyle X\to Y} is true if Y is a subset of X , so this type of dependence is called "trivial".
Trivial Graph. A trivial graph is the graph which has only one vertex. Example. In the above graph, there is only one vertex 'v' without any edge. Therefore, it is a trivial graph. 3. Simple Graph. A simple graph is the undirected graph with no parallel edges and no loops.
Trivial Graph in Graph Theory A graph with only one vertex is known as a trivial graph. In the above image, we see only one node and edges arising from it, thus it is a trivial graph.
