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A k-regular bipartite graph is the one in which degree of each vertices is k for all the vertices in the graph. Given that the bipartitions of this graph are U and V respectively. What is the relation between them?(a) Number of vertices in U=Number of vertices in V(b) Number of vertices in U not equal to number of vertices in V(c) Number of vertices in U always greater than the number of vertices in V(d) Nothing can be saidThe question was posed to me in unit test.Question is from Bipartite Graphs topic in portion Bipartite Graphs of Data Structures & Algorithms II

Answer»

Right CHOICE is (a) NUMBER of vertices in U=Number of vertices in V

Easiest EXPLANATION - We KNOW that in a bipartite graph sum of DEGREES of vertices in U=sum of degrees of vertices in V. Given that the graph is a k-regular bipartite graph, we have k*(number of vertices in U)=k*(number of vertices in V).



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