This PowerPoint contains introduction some special graphs like wheel, cycle, complete, bipartite , complete bipartite graph, regular graph

1. SPECIAL GRAPH
Mr. S.L. Khairnar

2. Special Graphs

3. 1) Complete Graph

4. A simple graph with n vertices in
which there is exactly one edge
between every pair of vertices.
It is denoted by 𝐾 𝑛

5. 2) Cycle

6. A simple graph containing n
vertices {𝑣1, 𝑣2 … . 𝑣 𝑛} and edges
{𝑣1, 𝑣2} , {𝑣2, 𝑣3} ,…. {𝑣 𝑛−1, 𝑣 𝑛} ,
{𝑣 𝑛, 𝑣1} . It is denoted by 𝐶 𝑛

7. 3) Wheels
15/08/2020

8. A simple graph obtained from
cycle Cn by adding an additional
vertex to a cycle Cn, and
connecting this new vertex to
each of the n vertices in Cn, by
new edges. It is denoted by 𝑊𝑛

9. Find the number of edges in i) Kn ii) Cn iii) Km;n iv) Wn v) Qn
Hint : Use Handshaking lemma and degree of vertex

10. 4) Bipartite Graph

11. A simple graph G is called bipartite if its vertex set
V can be partitioned into two disjoint sets V1and
V2 such that every edge in the graph connects a
vertex in V1 and a vertex in V2 (so that no edge in
G connects either two vertices in V1 or two
vertices in V2). When this condition holds, we call
the pair (V1, V2) a bipartition of the vertex set V
of G.

12. Find the number of edges in i) Kn ii) Cn iii) Km;n iv) Wn v) Qn
Hint : Use Handshaking lemma and degree of vertex

13. 5) Complete Bipartite
Graph

14. A complete bipartite graph (Km;n) is a graph that
has its vertex set partitioned into two subsets of m
and n vertices, respectively with an edge between
two vertices if and only if one vertex is in the first
subset and the other vertex is in the second
subset. It is denoted by 𝐾 𝑚,𝑛

15. Find the number of edges in i) Kn ii) Cn iii) Km;n iv) Wn v) Qn
Hint : Use Handshaking lemma and degree of vertex

16. 6) Hypercube

17. Hypercube constructed from the disjoint
union of two hypercubes Qn-1, by adding
an edge from each vertex in one copy of
Qn-1 to the corresponding vertex in the
other copy,𝑄 𝑛

18. Find the number of edges in i) Kn ii) Cn iii) Km;n iv) Wn v) Qn
Hint : Use Handshaking lemma and degree of vertex

19. 7) Regular

20. A graph G is said to be regular if
degree of all vertices is same.
If degree is k then it is called as
k-regular graph

21. Find the number of edges in i) Kn ii) Cn iii) Km;n iv) Wn v) Qn
Hint : Use Handshaking lemma and degree of vertex