What is the largest number of vertices in a graph with 24 edges and all vertices of the same degree?
The number of edges is one-half the sum of the degrees. Thus the number n of vertices can be no larger than 70/3. Since n is an integer, it can be no larger than 23.
How many edges does a regular graph with n vertices have?
A graph on n vertices that is k-regular has kn/2 edges (because the sum of the degrees is kn = 2*# of edges). If k is odd, then n has to be even in order for that fraction kn/2 to be an integer.
What is the maximum degree possible in a simple graph of n vertices?
11.1. 20 – In a graph with n vertices, the highest degree possible is n − 1 since there are only n − 1 edges for any particular vertex to be adjacent to.
How do you find the number of vertices on a simple graph?
Simple Graph The number of simple graphs possible with ‘n’ vertices = 2nc2 = 2n(n-1)/2.
What is the sum of the degrees of any tree of n vertices?
Hence, for a tree with n vertices and n – 1 edges, sum of all degrees should be 2 * (n – 1).
Does there exist a graph with n vertices and the maximum possible number of edges?
In a directed graph having N vertices, each vertex can connect to N-1 other vertices in the graph(Assuming, no self loop). Hence, the total number of edges can be are N(N-1). There can be as many as n(n-1)/2 edges in the graph if not multi-edge is allowed.
What is the maximum number of edges possible in a simple graph with n vertices such that there is no circuit of even length?
The maximum number of edges possible in a single graph with ‘n’ vertices is nC2 where nC2 = n(n – 1)/2.
For what value of n is KN regular?
Answer Expert Verified Kn is always regular for all n .. graph of degree n-1. Wn is regular for n = 3 .
What is an n regular graph?
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each vertex are equal to each other.
What is the maximum degree a simple graph with 5 vertices can have?
A simple graph has no loops or parallel edges. So, out of the total n vertices, all the vertices except the vertex itself (n-1 vertices) can be adjacent (have an edge) to this vertex. So, it’s degree can be maximum n-1.
How many simple graphs are there on n vertices?
A graph with no loops and no parallel edges is called a simple graph. The maximum number of edges possible in a single graph with ‘n’ vertices is nC2 where nC2 = n(n – 1)/2. The number of simple graphs possible with ‘n’ vertices = 2nc2 = 2n(n-1)/2.
How many edges can a graph with n vertices have?
The maximum number of edges a graph with N vertices can contain is X = N * (N – 1) / 2. XC0 + XC1 + XC2 + … + XCX = 2X. Graph Theory – Types of Graphs There are various types of graphs depending upon the number of vertices, number of edges, interconnectivity, and their overall structure.
Are there regular graphs with 24 edges that are 1-regular?
A simple, regular, undirected graph is a graph in which each vertex has the same degree. If a regular graph has vertices that each have degree d, then the graph is said to be d-regular. You are asking for regular graphs with 24 edges. Are there any regular graphs with 24 edges that are 1-regular? Yes. Consider the graph below:
How do you find the number of vertices of an odd graph?
For a K Regular graph, if K is odd, then the number of vertices of the graph must be even. Lets assume, number of vertices, N is odd. Sum of degree of all the vertices = 2 * Number of edges of the graph …….
What is a graph with no loops and no parallel edges?
A graph with no loops and no parallel edges is called a simple graph. The maximum number of edges possible in a single graph with ‘n’ vertices is n C 2 where n C 2 = n (n – 1)/2. The number of simple graphs possible with ‘n’ vertices = 2 nc2 = 2 n (n-1)/2.