In paper (1)

D. Frank Hsu proposed the notion of strongly harmoniouslabelings of graphs. There are three purposes in this paper:1. Compute the numbers of all strongly harmonious labelings of graphs with n edges. Obtain the followi result: [(n/2)!]2 n even ((n+1)/2)!((n-1)/2)! n odd2. Show several sorts of graphs which have no strongly

harmonious labelings

for examples: all trees but stars

all bipartite graphs but stars and Kn(n≥ 5)

etc. And we have proved that there are only two stroagly harmonious graphs in 3-regular graphs.3

Construct larger strongly harmonious graphs from a given one.