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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.
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.
How do you describe the size and location of three cubes on a graph?
For the size you can give the length of a side. For the location you need to identify the location of three vertices that are not coplanar or the two diagonally opposite vertices.
Write adjacency and incidence matrix for all the graphs developed?
adjacency matrix- since the edges are the relationship between two vertices ,the graph can be represented by a matrix,
How many edges must a simple graph with n vertices have in order to guarantee that it is connected?
The non-connected graph on n vertices with the most edges is a complete graph on n-1 vertices and one isolated vertex. So you must have one more than (n-1)n/2 edges to guarantee connectedness. It is easy to see that the extremal graph must be the union of two disjoint cliques (complete graphs). (Proof:In a non-connected graph with parts that are not cliques, add edges to each part until all are cliques. You will not have changed the number of parts. If there are more than two disjoint cliques, you can join cliques [add all edges between them] until there are only two.) It is straightforward to create a quadratic expression for the number of edges in two disjoint cliques (say k vertices in one clique, n-k in the other). Basic algebra will show that the maximum occurs when k=1 or n-1. (We're not allowing values outside that range.)
