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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 weekly connected graph?

A weekly connected graph is a type of directed graph in which, for every pair of vertices, there exists a path between them when ignoring the direction of the edges. This means that while the graph may have directed edges, it is possible to traverse from any vertex to any other vertex through a series of edges, regardless of their direction. However, unlike a strongly connected graph, the paths are not required to respect the direction of the edges. In essence, a weekly connected graph ensures that all vertices are part of a single connected component when treated as an undirected graph.


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 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 is the largest number of vertices in a graph with 35 edges if all vertices are of degree at least 3?

11......


What are parallel edges?

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


What shapes a line drawn between 2 verticels which are not next to each other?

A line drawn between two non-adjacent vertices in a graph or geometric shape is typically referred to as a diagonal. This line represents the shortest path connecting the two vertices, bypassing any intervening vertices or edges. The properties of this line, such as its length and direction, can be influenced by the overall structure of the shape or graph in which the vertices are located.


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.


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.