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- A non-trivial graph is any graph that contains more than one vertex. In other words, it consists of at least two distinct points (vertices) that may or may not be connected by edges. Non-trivial graphs exhibit a more complex structure with a higher degree of connectivity between their vertices compared to trivial graphs.
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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.
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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.
Terminology. A non-trivial graph consists of one or more vertices (or nodes) connected by edges. Each edge connects exactly two vertices, although any given vertex need not be connected by an edge. The degree of a vertex is the number of edges connected to that vertex.
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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.
- 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...
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related".
Aug 3, 2023 · Q1: What is a non-trivial graph in graph theory? A non-trivial graph is any graph that contains more than one vertex. In other words, it consists of at least two distinct points (vertices) that may or may not be connected by edges.
