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How do you write digraph in a sentence?

A digraph is short for directed graph.


When does a graph becomes a tree?

A graph becomes a tree when it is connected and acyclic, meaning there are no loops or cycles present. Additionally, for a graph with ( n ) vertices to be a tree, it must contain exactly ( n-1 ) edges. This structure ensures that there is exactly one path between any two vertices, fulfilling the properties of a tree.


What is a tree in graph theory?

In graph theory, a tree is a connected, acyclic graph, meaning it has no cycles and there is exactly one path between any two vertices. A tree with ( n ) vertices has exactly ( n - 1 ) edges. Trees are often used to represent hierarchical structures, such as organizational charts or family trees. Additionally, a special type of tree called a "rooted tree" has one designated vertex as the root, from which all other vertices can be reached.


What is a continuous path in a graph connecting all vertices that passes through every edge exactly once?

A continuous path in a graph that connects all vertices and passes through every edge exactly once is known as an Eulerian path. For a graph to have an Eulerian path, it must either have zero or two vertices of odd degree; if it has zero, the path is also an Eulerian circuit, which starts and ends at the same vertex. In contrast, if there are two vertices of odd degree, the path will start at one of these and end at the other. Euler's theorem provides the conditions necessary for the existence of such paths.


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 subgraph in given graph?

If all the vertices and edges of a graph A are in graph B then graph A is a sub graph of B.


How does the concept of a vertex cover relate to the existence of a Hamiltonian cycle in a graph?

In graph theory, a vertex cover is a set of vertices that covers all edges in a graph. The concept of a vertex cover is related to the existence of a Hamiltonian cycle in a graph because if a graph has a Hamiltonian cycle, then its vertex cover must include at least two vertices from each edge in the cycle. This is because a Hamiltonian cycle visits each vertex exactly once, so the vertices in the cycle must be covered by the vertex cover. Conversely, if a graph has a vertex cover that includes at least two vertices from each edge, it may indicate the potential existence of a Hamiltonian cycle in the graph.


How can i use a graph to find the number of vertices in a octagonal pyramid?

To find the number of vertices in an octagonal pyramid using a graph, you can represent the pyramid as a 3D shape with vertices, edges, and faces. An octagonal pyramid has 8 vertices, one at the top (apex) and 8 at the base. You can also draw a graph with each vertex representing a corner of the pyramid and each edge representing a line connecting two vertices. By counting the number of vertices in the graph representation, you can determine that an octagonal pyramid has a total of 9 vertices.


What is an adjacency list in the context of data structures and how is it used to represent relationships between vertices in a graph?

An adjacency list is a data structure used to represent relationships between vertices in a graph. It consists of a list of vertices, where each vertex has a list of its neighboring vertices. This allows for efficient storage and retrieval of information about the connections between vertices in a 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 cycle size of the given graph?

The cycle size of a graph is the number of vertices in the smallest cycle in the graph.


What is a drawing graph?

A drawing of a graph or network diagram is a pictorial representation of the vertices and edges of a graph. This drawing should not be confused with the graph itself: very different layouts can correspond to the same graph. In the abstract, all that matters is which pairs of vertices are connected by edges.