How do you know if a graph is self-complementary?

A graph is self-complementary if it is isomorphic to its complement. (i.e., G G ) For example the path P4 on 4 vertices and the cycle C5 on five vertices are self- complementary. Prove: If G is self-complementary on n vertices, then n 1 mod 4 or n 0 mod 4 .

What is meant by self-complementary?

A single strand of DNA that curls back onto itself is described as self-complementary.

Is there a self-complementary simple undirected graph with 4k 2 vertices?

There are no self-complementary on 4k + 2 or 4k + 3 vertices for all k = 0, 1, 2.. The sequence of number of non-isomorphic graphs on n vertices for n = 1, 4, 5, 8, 9, 12, 13, 16… is as follows: 1, 1, 2, 10, 36, 720, 5600, 703760.

Which of the following can be the vertices in a self-complementary graph?

As there are self-complementary graphs on 1 vertex and on 4 vertices, it follows that, for any n=0,1(mod4) there is a self-complementary graph on n vertices.

What is the complement of a graph?

In graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices of H are adjacent if and only if they are not adjacent in G.

Does there exist a disconnected self-complementary graph?

Self-complementary graphs are those which are isomorphic to their complements. Isomorphic condition would be broken if the number of connected components change between the graph and it’s complement. Hence there can’t be a disconnected self-complementary graph.

What is 2421 BCD code?

The Aiken code (also known as 2421 code) is a complementary binary-coded decimal (BCD) code. A group of four bits is assigned to the decimal digits from 0 to 9 according to the following table.

Can a graph be self-complementary?

A self-complementary graph is a graph which is isomorphic to its complement. The simplest non-trivial self-complementary graphs are the 4-vertex path graph and the 5-vertex cycle graph. There is no known characterization of self-complementary graphs.

What is a cycle graph theory?

In graph theory, a cycle in a graph is a non-empty trail in which the only repeated vertices are the first and last vertices. A directed cycle in a directed graph is a non-empty directed trail in which the only repeated vertices are the first and last vertices. A graph without cycles is called an acyclic graph.

How do you complement a graph?

That is, to generate the complement of a graph, one fills in all the missing edges required to form a complete graph, and removes all the edges that were previously there. The complement is not the set complement of the graph; only the edges are complemented.

How do you prove a graph is connected?

Given a graph with n vertices, prove that if the degree of each vertex is at least (n−1)/2 then the graph is connected. The distance between two vertices in a graph is the length of the shortest path between them. The diameter of a graph is the distance between the two vertices that are farthest apart.

How do I find my BCD code?

Simply divide the binary number into groups of four digits, starting with the least significant digit and then write the decimal digit represented by each 4-bit group.