Are complete graphs strongly regular graphs?
Strongly regular graphs were introduced by R.C. Bose in 1963. Some authors exclude graphs which satisfy the definition trivially, namely those graphs which are the disjoint union of one or more equal-sized complete graphs, and their complements, the complete multipartite graphs with equal-sized independent sets.
What is a 5 regular graph?
Definition: A graph G is 5-regular if every vertex in G has degree 5.
How many vertices are in a graph?
A graph is a diagram of points and lines connected to the points. It has at least one line joining a set of two vertices with no vertex connecting itself. The concept of graphs in graph theory stands up on some basic terms such as point, line, vertex, edge, degree of vertices, properties of graphs, etc.
How do you know if a graph is regular?
A graph is called regular graph if degree of each vertex is equal. A graph is called K regular if degree of each vertex in the graph is K.
How many strongly normal graphs are there?
, there are exactly seven known connected triangle-free strongly regular graphs, as summarized in the following table (Godsil 1995) and six of which are illustrated above.
What is difference between complete graph and regular graph?
In a complete graph of N vertices, each vertex is connected to all (N-1) remaining vertices. For a K regular graph, each vertex is of degree K. Sum of degree of all the vertices = K * N, where K and N both are odd.So their product (sum of degree of all the vertices) must be odd.
What is a 4 regular graph?
From Wikipedia, the free encyclopedia. In the mathematical field of graph theory, a quartic graph is a graph where all vertices have degree 4. In other words, a quartic graph is a 4-regular graph.
When is a graph said to be strongly regular?
G is said to be strongly regular if there are also integers λ and μ such that: Every two adjacent vertices have λ common neighbours. Every two non-adjacent vertices have μ common neighbours. A graph of this kind is sometimes said to be an srg ( v, k, λ, μ).
How many vertices are in a regular graph?
Degree of each vertices of this graph is 2. So, the graph is 2 Regular. Similarly, below graphs are 3 Regular and 4 Regular respectively. A complete graph N vertices is (N-1) regular. In a complete graph of N vertices, each vertex is connected to all (N-1) remaining vertices.
When is G said to be strongly regular?
G is said to be strongly regular if there are also integers λ and μ such that: Every two adjacent vertices have λ common neighbours. Every two non-adjacent vertices have μ common neighbours.
Which is the complement of a strongly regular graph?
The complement of an srg ( v, k, λ, μ) is also strongly regular. It is an srg ( v, v−k −1, v −2−2 k +μ, v −2 k +λ). A strongly regular graph is a distance-regular graph with diameter 2 whenever μ is non-zero.