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This book is based on the two pioneering works on the relationship between minimum rank and path cover number of a graph. We have tried to understand and work out the results obtained from the two research papers. The relationship between the minimum rank of a tree to its several invariants including the path cover number has been worked out from the first paper. Formulae for the minimum rank of vertex sums of graphs and formulae for the minimum rank and path cover number for graphs obtained from edge-sums have been derived from the second paper.