Graceful labeling of friendship graph

125 Views Asked by At

I read the Wikipedia page of Friendship Graph which says that it is graceful if and only if its number of cycles is 0 or 1 mod 4.

The right direction is obvious by Rosa, but I cannot seem to construct the labeling. I manage to find it only when the graph has 4 cycles or 8 cycles, but even so I cannot make the general labeling.

I also cannot find the origin paper from Bermond et al. Hence I come here to hopefully get some hints to construct the labeling or maybe a link where I can learn more specifically on the gracefulness of this graph? Thanks in advance.