Problem 4: The parts (a) and (b) of this problem are independent of each other. G1 G2 6 (a) Prove that the graphs G1 and G2 are isomorphic by exhibiting an isomorphism from one to the other by concrete arguments and verify it by using adjacency matrices. Please take the ordering of the vertices as 1,2,3, 4, 5,6 while forming Ac,, adjacency matrix of 2.
The parts (a) and (b) of this problem are independent
of each other.
G1 G2
4 5
1 2
3
6
s
x y
t u v
(a) Prove that the graphs G1 and G2 are isomorphic by
exhibiting an isomorphism from one to the other by
concrete arguments and verify it by using adjacency
matrices. Please take the ordering of the vertices as
1, 2, 3, 4, 5, 6 while forming AG1
, adjacency matrix of
G1.
Warning: One must stick to the labelings of
the vertices as they are given, if one changes
the labelings/orderings etc., the solution will
not be taken into account.
(b) Consider the complete graph K13 with vertex set
V13 = {u1, u2, u3, · · · , u13}.
Let H = (V, E) be the simple graph obtained from
K13 by adding a new vertex u, i.e. V = V13 ∪ {u}
and deleting the edges {u1, u2} and {u2, u3} and
adding the edges {u1, u} and {u, u2} and keeping
the remaining edges same.
Determine whether H has an Euler circuit or not,
an Euler path or not. One must validate any conclusion by clear arguments.
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