For a given graph, the “Node Coloring Problem” is to find a way to color all the nodes using the smallest possible numbe

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For a given graph, the “Node Coloring
Problem” is to find a way to color all the nodes using the smallest
possible number of different colors, such that no two adjacent
nodes have the same color. Now, given a graph of nodes
and let be the smallest needed number of different
colors. Clearly, .
(i) What type of graph has the
largest possible number ? In this case, what is (in
terms of )? ___100_____
(ii) For a perfect ring
with nodes, is at least _____ and at most
____
(iii) For a Hamiltonian graph
with nodes, is at least ______ and at most
______
(iv) Show 2 different types of
graphs with nodes, which have :
1) __________ 2) __________
(v) For the fractal shown below, which
continues to grow bigger and bigger, where each corner is a
node: is at least ______ and at most ______