How many vertices can a self-complementary graph have?
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.
How do you prove a graph is self-complementary?
graphs with 4k f 1 vertices which have this graph as an induced subgraph. Simply connect the new vertex to alternate vertices in each cycle of p. By the Construction Algorithm, this new graph will be self- complementary.
For what values of Na graph with n vertices can be self-complementary?
Explanation: An n-vertex self-complementary graph has exactly half number of edges of the complete graph, i.e., n(n − 1)/4 edges, and (if there is more than one vertex) it must have diameter either 2 or 3.
How do you find the complementary graph?
It means, two vertices are adjacent in ‘G−’ if the two vertices are not adjacent in G. If the edges that exist in graph I are absent in another graph II, and if both graph I and graph II are combined together to form a complete graph, then graph I and graph II are called complements of each other.
What is self complementing code give example?
Now, the sum of (11)10 + (4)10 = (15)10, and not (9)10. Therefore, we conclude that 1011 and 0100 are not complementary numbers and hence, the conventional binary code is not a self-complementing code. Example 25: Prove that 2-4-2-1 code is a self-complementing code….Self Complementing Codes.
| 2-4-2-1 Code | Decimal equivalent |
|---|---|
| 1101 | 7 |
| 1110 | 8 |
| 1111 | 9 |
What is the maximum degree of any vertex in simple graph with n vertices?
A simple graph having no loops or parallel edges. So, out of total n vertices, all the vertices except the vertex itself (n-1 vertices) can be adjacent (have an edge) to this vertex. So, its degree can be maximum n-1.
What does self-complementary mean?
Self-complementarity is the likelihood that the primer will bind to itself and to the other primer in the pair. Self 3′-complementarity is the likelihood that the primer will bind to itself and to the other primer in the pair at the 3′ end.
Is P5 self-complementary?
Then a minimum coloring is produced. (Actually the theorem in [2] is proved for a larger class of graphs.) Note that the class of (C5,P5, house)-free graphs is self-complementary, so Theorem 1. 5 can also be used to find a minimum clique cover.
Which of the following graphs is 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.
Is Petersen graph self complementary?
The Petersen graph is the complement of the line graph of K5. It is also the Kneser graph KG5,2; this means that it has one vertex for each 2-element subset of a 5-element set, and two vertices are connected by an edge if and only if the corresponding 2-element subsets are disjoint from each other.
What does self complementing mean?
Self complementing codes are the codes that have the property that 9’s complement of a decimal no. is obtained directly by replacing 1s by 0s and 0s by 1s i.e. by complementing each bit in the pattern.