Question: Let G = (V, E) be a graph with V = {v1, V2, ..., Un}. Let Ac be its adjacenty matrix. Consider the matrix B

Let G = (V, E) be a graph with V = {v1, V2, ..., Un}. Let Ac be its adjacenty matrix. Consider the matrix B = (bij)=1 given by B := (AG)2 (i) Find the trace of B (ii) Let G' = (V, E' ) be the graph whose edges correspond to nonzero off-diagonal entries of B: E' := {{viv;} |i * j such that bij # 0} For which graphs G will G' be connected

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