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What is directed multigraph?
multigraph is graph it is connect multi edge
What is a cycle graph?
A cycle is a closed path such that the end vertex of the final edge is the start vertex of the first edge.
What is cyclomatic number of a graph is called?
cyclomatic number of a graph is e.n+1 where e is number of edge of graph and n is number of node in graoh g
What is the automorphism group of a complete bipartite graph?
The automorphism group of a complete bipartite graph K_n,n is (S_n x S_n) semidirect Z_2.
What degree of a vertex would lead to a vertex edge graph unable to be traveled?
2
What is the articulation point in a graph and how does it impact the overall connectivity of the graph?
The articulation point in a graph is a vertex that, when removed, increases the number of connected components in the graph. It impacts the overall connectivity by serving as a critical point that, if removed, can break the graph into separate parts, affecting the flow of information or connectivity between different parts of the graph.
Is the complete graph on 5 vertices planar?
No, the complete graph of 5 vertices is non planar. because we cant make any such complete graph which draw without cross over the edges . if there exist any crossing with respect to edges then the graph is non planar.Note:- a graph which contain minimum one edge from one vertex to another is called as complete graph...
What are the properties of an irreducible graph and how does it impact the connectivity of the graph?
An irreducible graph is a graph where every pair of vertices is connected by a path. This means that there are no isolated vertices or disconnected components in the graph. The property of irreducibility ensures that the graph is connected, meaning that there is a path between any two vertices in the graph. This connectivity property is important in analyzing the structure and behavior of the graph, as it allows for the study of paths, cycles, and other connectivity-related properties.
What is the clique problem and how does it relate to graph theory?
The clique problem is a computational problem in graph theory where the goal is to find a subset of vertices in a graph where every pair of vertices is connected by an edge. This subset is called a clique. In graph theory, cliques are important because they help us understand the structure and connectivity of a graph. The clique problem is a fundamental problem in graph theory and has applications in various fields such as computer science, social networks, and biology.
What is the significance of a minimum spanning tree in the context of a graph and how does it impact the overall structure and connectivity of the graph?
A minimum spanning tree in a graph is a tree that connects all the vertices with the minimum possible total edge weight. It is significant because it helps to find the most efficient way to connect all the vertices while minimizing the total cost. This impacts the overall structure and connectivity of the graph by ensuring that all vertices are connected in the most optimal way, which can improve efficiency and reduce costs in various applications such as network design and transportation planning.
Difference between a directed graph and an undirected graph in a computer program?
In an undirected graph, an edge is an unordered pair of vertices. In a directed graph, an edge is an ordered pair of vertices. The ordering of the vertices implies a direction to the edge, that is that it is traversable in one direction only.
What is the significance of perfect matching in a bipartite graph and how does it impact the overall structure and connectivity of the graph?
In a bipartite graph, a perfect matching is a set of edges that pairs each vertex in one partition with a unique vertex in the other partition. This is significant because it ensures that every vertex is connected to exactly one other vertex, maximizing the connectivity of the graph. Perfect matching plays a crucial role in determining the overall structure and connectivity of the bipartite graph, as it helps to establish relationships between different sets of vertices and can reveal important patterns or relationships within the graph.
What is the significance of strongly connected components in a graph and how do they contribute to the overall structure and connectivity of the graph?
Strongly connected components in a graph are groups of vertices where each vertex can be reached from every other vertex within the same group. These components play a crucial role in understanding the connectivity and structure of a graph. They help identify clusters of closely connected nodes, which can reveal important patterns and relationships within the graph. By identifying strongly connected components, we can better understand the overall connectivity and flow of information in the graph, making it easier to analyze and manipulate the data.
Is it possible for the majority of a graph to contain the largest weighted edge?
Yes, it is possible for the majority of a graph to contain the largest weighted edge.
What is the difference between a node and an edge in a graph theory context?
In graph theory, a node (or vertex) represents a point or entity in a graph, while an edge represents a connection or relationship between two nodes.
What is the significance of a Hamiltonian cycle in a bipartite graph and how does it impact the overall structure and connectivity of the graph?
A Hamiltonian cycle in a bipartite graph is a cycle that visits every vertex exactly once and ends at the starting vertex. It is significant because it provides a way to traverse the entire graph efficiently. Having a Hamiltonian cycle in a bipartite graph ensures that the graph is well-connected and has a strong structure, as it indicates that there is a path that visits every vertex without repeating any. This enhances the overall connectivity and accessibility of the graph, making it easier to analyze and navigate.
What is the bottom edge of a line graph?
The x-axis
