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Bipartite Graph:
A graph is bipartite if its vertex set can be partitioned into two subsets X and Y so that every edge has one end in X and one end in Y; such a partition (X,Y) is called bipartition of the graph, and X and Y its parts.
ex.-
Notation:
We denote a bipartite graph G with bipartition (X,Y) by G[X,Y].
Complete Bipartite Graph:
If G[X,Y] is simple and every vertex in X is joined to every vertex in Y, then G is called a Complete Bipartite graph.
ex.-
Semi-Hamiltonian Graph:
A semi-Hamiltonian graph is a graph that contains a Hamiltonian path, but not a Hamilton cycle.
Hamiltonian Path:
A Hamiltonian path in an undirected or directed graph is a path which visits each vertex exactly once.
ex.- C-A-D-B-E is a Hamiltonian path
Hamiltonian Cycle:
A Hamiltonian cycle or a Hamiltonian Circuit is a Hamiltonian path which is a cycle.
This post will be useful in understanding a question: "The nabhi kamal grapg is:"
(A)Bipartite graph
(B)Semi-Hamiltonian graph
(C)Both (A) and (B)
(D) Neither (A) nor (B)
(This question was asked in SET Paper -II Question 3.examination for subject Computer Science and Applications in paper AUG 37211/II)
A graph is bipartite if its vertex set can be partitioned into two subsets X and Y so that every edge has one end in X and one end in Y; such a partition (X,Y) is called bipartition of the graph, and X and Y its parts.
ex.-
Notation:
We denote a bipartite graph G with bipartition (X,Y) by G[X,Y].
Complete Bipartite Graph:
If G[X,Y] is simple and every vertex in X is joined to every vertex in Y, then G is called a Complete Bipartite graph.
ex.-
A semi-Hamiltonian graph is a graph that contains a Hamiltonian path, but not a Hamilton cycle.
Hamiltonian Path:
A Hamiltonian path in an undirected or directed graph is a path which visits each vertex exactly once.
ex.- C-A-D-B-E is a Hamiltonian path
Hamiltonian Cycle:
A Hamiltonian cycle or a Hamiltonian Circuit is a Hamiltonian path which is a cycle.
This post will be useful in understanding a question: "The nabhi kamal grapg is:"
(B)Semi-Hamiltonian graph
(C)Both (A) and (B)
(D) Neither (A) nor (B)
(This question was asked in SET Paper -II Question 3.examination for subject Computer Science and Applications in paper AUG 37211/II)
Excellent explaination.
ReplyDeleteMay It be useful for the Preparation
I had this query. Thank you for the explanation.
ReplyDeleteVery good blog post !!! Waiting for your next blog !!
ReplyDeleteA Great Post....
ReplyDeleteGreat explanation! !
ReplyDeleteGreat ...would like to see you teaching students ... inspirations :-)
ReplyDelete