A graph is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of paired vertices, whose elements are called edges (sometimes links or lines). Note that, a graph is a 1-dimensional simplicial complex. A graph be connected graph if there is a path from x to y for any two vertices x and y. a) What are the possible homology groups of a connected graph? Explain your answer (no strict proof needed). b) Use a) to classify the homotopy type of a connected graph.