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19. (a) For which values of m and n is the complete bipartite graph Km.n a tree? (b) For which values n is the complete graph K, a tree?

19. (a) For which values of m and n is the complete bipartite graph Km.n a tree? (b) For which values n is the complete graph K, a tree?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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19-
(d) Antisymmetric YES NO (e) Irreflexive YES NO (f) Asymmetric YES NO or) el (0) 18. (a) How many simple non-isomorphic simple undirected graphs with five vertices and three edges are there? Draw them all (hint: less than 10) (b) How many simple non-isomorphic directed graphs with five vertices and three edges are there? Draw them all. (hint: less than 20) 19. (a) For which values of m and n is the complete bipartite graph Km.n a tree? (b) For which values n is the complete graph K, a tree? 20. Prove: A bipartite graph with an odd number of vertices does NOT have a Hamilton Circuit.
Transcribed Image Text:(d) Antisymmetric YES NO (e) Irreflexive YES NO (f) Asymmetric YES NO or) el (0) 18. (a) How many simple non-isomorphic simple undirected graphs with five vertices and three edges are there? Draw them all (hint: less than 10) (b) How many simple non-isomorphic directed graphs with five vertices and three edges are there? Draw them all. (hint: less than 20) 19. (a) For which values of m and n is the complete bipartite graph Km.n a tree? (b) For which values n is the complete graph K, a tree? 20. Prove: A bipartite graph with an odd number of vertices does NOT have a Hamilton Circuit.
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