# Discrete Math

1) Let $T$ be a tree with 47 vertices with the property that removing a vertex (and its adjacent edges) from $T$ creates two coherent components $T_1,T_2$ which are also trees. For$i=1,2,$ we denote by Vi the number of vertices of Ti and by Ei the number of edges of $T_i$ . If $|V1|=|E2|+7$ find $|V1|$.

2) From image 1,2 find if they are Eulerian and Hamiltonian Graphs for each of them.

3) Consider the graph G with vertices $\{2,3,6,7,9,10,11,22\}$ and edges the pairs ${i,j}$ for which greatest_common_divisor$(i,j)?1$
How many coherent components does G have? (Hint: draw the graph and measure the coherent components).

• What makes a component "coherent"? Is that a synonym for "connected"?

• coherent means connected yes. Thats the meaning

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