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What is the largest number of vertices in a graph with 35 edges if all vertices are of degree at least 3?
11......
What is the largest number of vertices in a graph with 35 edges if all vertices areof degree at least 3?
Abe sale dimag kharab mat kar samjha>>>>>>>>>>>>>>>>
How can you show that every Hamiltonian cubic graph is 3-edge-colorable?
A cubic graph must have an even number of vertices. Then, a Hamilton cycle (visiting all vertices) must have an even number of vertices and also an even number of edges. Alternatively color this edges red and blue, and the remaining edges green.
What is the sum of degrees of all vertices in an undirected graph is twice the number of edges?
It is a true statement.
Can there be a graph with 8 vertices and 29 edges?
Yes.
What is the largest number of vertices in a graph with 35 edges if all vertices are of degree at least 3?
11......
What is the largest number of vertices in a graph with 35 edges if all vertices areof degree at least 3?
Abe sale dimag kharab mat kar samjha>>>>>>>>>>>>>>>>
What is the largest number of vertices in a graph with 35 edges is all vertices are of degree at least 3?
In a graph, the sum of the degrees of all vertices is equal to twice the number of edges. This is known as the Handshaking Lemma. Therefore, if all vertices in a graph with 35 edges have a degree of at least 3, the sum of the degrees of all vertices must be at least 3 times the number of vertices. Since each edge contributes 2 to the sum of degrees, we have 2 * 35 = 3 * V, where V is the number of vertices. Solving for V, we get V = 70/3 = 23.33. Since the number of vertices must be a whole number, the largest possible number of vertices in this graph is 23.
How can you show that every Hamiltonian cubic graph is 3-edge-colorable?
A cubic graph must have an even number of vertices. Then, a Hamilton cycle (visiting all vertices) must have an even number of vertices and also an even number of edges. Alternatively color this edges red and blue, and the remaining edges green.
How can we determine the number of cycles in a graph?
To determine the number of cycles in a graph, you can use the concept of Euler's formula, which states that for a connected graph with V vertices, E edges, and F faces, the formula is V - E F 2. By calculating the number of vertices, edges, and faces in the graph, you can determine the number of cycles present.
What is the significance of a minimum edge cover in graph theory and how does it impact the overall structure of a graph?
A minimum edge cover in graph theory is a set of edges that covers all the vertices in a graph with the fewest number of edges possible. It is significant because it helps identify the smallest number of edges needed to connect all the vertices in a graph. This impacts the overall structure of a graph by showing the essential connections between vertices and highlighting the relationships within the graph.
The minimum number of edges in a connected cyclic graph on n vertices is?
n-1
How many minimum edges in a Cyclic graph with n vertices?
The term "cyclic graph" is not well-defined. If you mean a graph that is not acyclic, then the answer is 3. That would be the union of a complete graph on 3 vertices and any number of isolated vertices. If you mean a graph that is (isomorphic to) a cycle, then the answer is n. If you are really asking the maximum number of edges, then that would be the triangle numbers such as n (n-1) /2.
What is the sum of degrees of all vertices in an undirected graph is twice the number of edges?
It is a true statement.
What is the maximum number of edges in an undirected graph with V vertices?
V*(V-1)/2
Can there be a graph with 8 vertices and 29 edges?
Yes.
What is the longest simple path that can be found in a given graph?
The longest simple path in a graph is the path that does not repeat any vertices and has the most number of edges between two distinct vertices.
