Question

2. a) Determine whether the following graphs are isomorphic or not. If so write an isomorphism, if not explain why. 1 b 2 a 6 3 f d 5 4 e Graph A Graph B. b) Is the graph A bipartite. If not, find a vertex v such that A - v bipartite? c) Does the graph A have an Eulerian circuit? If not find an edge e such that A - e has an Eulerian circuit.

Answer 1

But 3 if lue tomoue vertex berome A- than the graph Bipartite 6 IS A il ☺ Euleman circuit graph This is a circuit that travels ouer every edge and once and -slarte only ends in the same place once and

It is not a cualerias circuit 4. ed" бую Oasds) But a lo 3.0 лифма + ☺ aud3) a curlerion get thad de ссия 2 13. ч (5. Ч 2 2 6

2 4 deg. dega dege? deg 3 049 deg: 3 dege 2 deg: 2 dega Idege 2 deg = Cumph A Neces al Condition fou iso mouphism 5 deg - 3 Graph B. for must be same 11 Number of of veutices in both the in both the must be same uce of both the graph must k is the graph 2) Number edged graph must be same. Degree shequebec 4) ou a cycle Mentier { . . lx} eu one graph then a length cycle & f(a) fluo. fleece) }, au stuer the vertice same length k k must be of length formed by pershed by graph. vertices in Graph A = 6 (satisfy No. Craph B = 6 11 in Graph A=8 2) Number of edges (satisfy Curaph B = 8 11

3) degree ексе 1 degree sequen of peoph A graph B 2) $ 2, 3, 4, 5, 9, ва, 2, 3, 2, ы, 2 } Start from.) ( a + 1) aph contain same Both 3 Д чар cycle. graph may be exomorphic. Sufficient Condition Но онарь и до тоя рhte 9 оры the Complement of go do moupnei than must be

complement of A Complement of 6 3 5 Complements are not leloumporneo do. the graphs are not Gomorphie graph A Bip artite is a which consist graph graph vertices x and y and 2) Is the A Bipantite two dete of of join only The vertical of set x with the vertia Set y. and The vertices within the seeme set do not of jou (6 (4 Nota bipartite graph