Some work towards the proof of the reconstruction conjecture

In this paper we de2ne 2ve families of simple graphs {fi,f2,f^,t^ and F=5) such that the reconstruction conjecture is true if reconstruction is proved for either the families $[,$2 & % or the families F=3;F=4 and F=5. These families are quite restrictive in that each has diameter two or three. Then we prove that families F=1;F=2;F=3;F=4 and F=5 are recognizable by proving that graphs of diameter two and edge-minimal graphs of diameter two are recognizable. The reconstruction conjecture is thus reduced to showing weak reconstructibility for either of the two sets of families.