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Can there be a graph with 8 vertices and 29 edges?

Yes.


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.


What are the differences between the Floyd-Warshall and Bellman-Ford algorithms for finding the shortest paths in a graph?

The Floyd-Warshall algorithm finds the shortest paths between all pairs of vertices in a graph, while the Bellman-Ford algorithm finds the shortest path from a single source vertex to all other vertices. Floyd-Warshall is more efficient for dense graphs with many edges, while Bellman-Ford is better for sparse graphs with fewer edges.


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.


What is the shortest path in an undirected graph?

The shortest path in an undirected graph is the path between two vertices that has the smallest total sum of edge weights.


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 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.


What are parallel edges?

- Two or more edges that join the same pair of vertices in a graph. Also known as multiple edges.


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 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 shortest path with at most k edges between two points in a given graph?

The shortest path with at most k edges between two points in a graph is known as the k-shortest path. It is the path that has the fewest number of edges while still connecting the two points.


What is the largest number of vertices in a graph with 35 edges if all vertices are?

36 vertices if all of them are or order two except one at each end.