Some work towards the proof of the reconstruction conjecture

S.K. Gupta, Pankaj Mangal, Vineet Paliwal
2003 Discrete Mathematics  
In this paper we de2ne 2ve families of simple graphs {fi,f 2 ,f^,t^ and F= 5 ) such that the reconstruction conjecture is true if reconstruction is proved for either the families $[,$2 m & % 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
more » ... conjecture is thus reduced to showing weak reconstructibility for either of the two sets of families.
doi:10.1016/s0012-365x(03)00198-5 fatcat:3poesxtdk5chdedgon7fyx5ucy