| “ | The sum of the weights on every path of length k in a graph G with edges of weight 1 or -1 is called the Pk(G,w)-total weight of the ±1-assigned graph, with assignment w. The minimum of the absolute value of the Pk-total weights of a graph considering every possible ±1 assignment is called the minimum pk-total weight. This project is to study the boundaries of the minimum pk(G)-total weights for simple connected graphs. | ” |