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+1 vote

Are the two diagraphs shown in the above figure isomorohic? Justify your answer.

asked in Graph Theory by Veteran (112k points) | 262 views

3 Answers

+2 votes
since , all conditions like

no if points , no of edges, no of in degree and out degree sequences , no of cycle length all are same still they are necessary and  but not sufficient condition so we cant say at this point

for this if we map each vertex as one to one correspondence of both the graphs then they are isomorphic to each other

i.e. f(x5)=y4  , f(x4)=y5, f(x1)=(y2), f(x2)=y2, f(x3)=y3 , these one to one correspondence is done on the basis of thier no of in degree and no of out degree , since all vertices of both graphs matched so its isomorphic graph
answered by Active (4.9k points)
+1 vote
answered by (95 points)
edited by
+1 vote

Yes it is isomorphic

They have same no. Of vertices

They have same no. Of edges.

They have same no. Of degree

X5 and Y4 have same degree

Now try to draw adjacent nodes

answered by Junior (913 points)
I dont think these are isomporphic.. Analyse your figure carefully

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