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Assuming that each bridge can connect at most two vertices, you will need at least 4 bridges to connect seven vertices. Conversely, two bridges will connect at most four vertices.
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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 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.)
What does vertex mean in math terms?
vertex is a special point of a mathematical object, and is usually a location where two or more lines or edges meet. Vertices are most commonly encountered in angles, polygons, polyhedra, and graphs. Graph vertices are also known as nodes.
Does there exist a simple graph with 7 vertices having degrees 1 3 3 4 5 6 6?
No. Since the graph is simple, none of the vertices connect to themselves - that is, there are no arcs that loop back on themselves. Then the two vertices with degree 6 must connect to all the other vertices. Therefore there can be no vertex with less than two arcs [ to these two vertices]. So a vertex with degree 1 cannot be part of the graph.
A digraph is a graph with exactly two vertices. true or false?
false
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.
What is a bigraph?
A bigraph is another term for a bipartite graph - in mathematics, a graph whose vertices can be divided into two disjoint sets.
Prove that every tree with two or more vertices is bichromatic?
Prove that the maximum vertex connectivity one can achieve with a graph G on n. 01. Define a bipartite graph. Prove that a graph is bipartite if and only if it contains no circuit of odd lengths. Define a cut-vertex. Prove that every connected graph with three or more vertices has at least two vertices that are not cut vertices. Prove that a connected planar graph with n vertices and e edges has e - n + 2 regions. 02. 03. 04. Define Euler graph. Prove that a connected graph G is an Euler graph if and only if all vertices of G are of even degree. Prove that every tree with two or more vertices is 2-chromatic. 05. 06. 07. Draw the two Kuratowski's graphs and state the properties common to these graphs. Define a Tree and prove that there is a unique path between every pair of vertices in a tree. If B is a circuit matrix of a connected graph G with e edge arid n vertices, prove that rank of B=e-n+1. 08. 09.
Which platonic graph is Bipartite?
A cube is bipartite platonic graph. You can represent it as platonic by drawing one square inside another and connecting respective edges. Start from any vertex, name it A, color it black. Color the adjacent vertices red and name them B, C, D. Take one of the red vertices (i,e, B, C, D)and all adjacent vertices should be black... and so on. You will be able to get cube with no edges between two vertices of same color. This shows it should be bipartite as well as we used only two color to represent graph. Furthermore, put vertices of black and red color in two partitions and connect them with same edges as in the previous graph. Since, there is no edge between two vertices of same color this is bipartite graph as required.
How many subgraphs with at least one vertex does a complete graph of 3 vertices k3 have?
one vertex: 3 two vertices: 6 three vertices: 8 total 17
What is Difference between tree and spanning tree?
A tree is a connected graph in which only 1 path exist between any two vertices of the graph i.e. if the graph has no cycles. A spanning tree of a connected graph G is a tree which includes all the vertices of the graph G.There can be more than one spanning tree for a connected graph G.
What is a Line between two vertices called?
A line between 2 vertices in Graph theory is called an edge or an arc, although arc is usually used to denote a directed edge.
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.
What are parallel edges?
- Two or more edges that join the same pair of vertices in a graph. Also known as multiple edges.
What is the maximum number of distinct edges in an undirected graph with N vertices?
Let G be a complete graph with n vertices. Consider the case where n=2. With only 2 vertices it is clear that there will only be one edge. Now add one more vertex to get n = 3. We must now add edges between the two old vertices and the new one for a total of 3 vertices. We see that adding a vertex to a graph with n vertices gives us n more edges. We get the following sequence Edges on a graph with n vertices: 0+1+2+3+4+5+...+n-1. Adding this to itself and dividing by two yields the following formula for the number of edges on a complete graph with n vertices: n(n-1)/2.
