(a) C1 = { all graphs }: The smallest n for which C1 contains nonisomorphic n-vertex graphs with the same degree sequence is n=2. This is because a graph with two vertices can either be connected or disconnected, which are non-isomorphic structures with the same degree sequence (1,1).

(b) C2 = { loopless graphs }: The smallest n for which C2 contains nonisomorphic n-vertex graphs with the same degree sequence is n=3. This is because a graph with three vertices can either form a path (P3) or a cycle (C3), which are non-isomorphic structures with the same degree sequence (2,2,2).

(c) C3 = { simple graphs }: The smallest n for which C3 contains nonisomorphic n-vertex graphs with the same degree sequence is n=4. This is because a simple graph with four vertices can either form a path (P4) or a star (K1,3), which are non-isomorphic structures with the same degree sequence (1,1,2,3).

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(a) C1 = { all graphs }: The smallest n for which C1 contains nonisomorphic n-vertex graphs with the same degree sequence is n=2. This is because a graph with two vertices can either be connected or disconnected, which are non-isomorphic structures with the same degree sequence (1,1).

(b) C2 = { loopless graphs }: The smallest n for which C2 contains nonisomorphic n-vertex graphs with the same degree sequence is n=3. This is because a graph with three vertices can either form a path (P3) or a cycle (C3), which are non-isomorphic structures with the same degree sequence (2,2,2).

(c) C3 = { simple graphs }: The smallest n for which C3 contains nonisomorphic n-vertex graphs with the same degree sequence is n=4. This is because a simple graph with four vertices can either form a path (P4) or a star (K1,3), which are non-isomorphic structures with the same degree sequence (1,1,2,3).

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(a) C1 = { all graphs }: The smallest n for which C1 contains nonisomorphic n-vertex graphs with the same degree sequence is n=2. This is because a graph with two vertices can either be connected or disconnected, which are non-isomorphic structures with the same degree sequence (1,1).

(b) C2 = { loopless graphs }: The smallest n for which C2 contains nonisomorphic n-vertex graphs with the same degree sequence is n=3. This is because a graph with three vertices can either form a path (P3) or a cycle (C3), which are non-isomorphic structures with the same degree sequence (2,2,2).

(c) C3 = { simple graphs }: The smallest n for which C3 contains nonisomorphic n-vertex graphs with the same degree sequence is n=4. This is because a simple graph with four vertices can either form a path (P4) or a star (K1,3), which are non-isomorphic structures with the same degree sequence (1,1,2,3).

For each of the classes Ci below determine the smallest n for which Cicontains nonisomorphic n-vertex graphs with the same degree sequence:(a) C1 = { all graphs }, (b) C2 = { loopless graphs }, (c) C3 = { simplegraphs }

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