Every edge of G is missing from exactly two cards, thus each edge shows up on n-2 cards. The number of G can be determined by summing the numbers of edges on each card and dividing the total by n-2 . A parameter of G which can be deduced from the deck is called reconstructible . Since, the number of edges of G is reconstructible, the degree sequence of G is reconstructible. Thus, if G is a regular graph, G itself is reconstructible.
Disconnected graphs are reconstructible.
Trees are reconstructible. Separable graphs without endvertices are reconstructible. Years later, he heard in a lecture that the characteristic polynomial and chromatic number were not known to be reconstructible. Tutte also showed how to count the Hamilton cycles. A similar polynomial, called the idiosyncratic polynomial is also reconstructible.