## Abstract A strongly harmonious labeling is the nonmodular version of a harmonious labeling. The windmill graph __K__^(__t__^)~__n__~ is the graph consisting of __t__ copies of the complete graph __K~n~__ with a vertex in common. It is shown that, for __t__ ≥ 1, __K__^(__t__^)~__n__~ is strongly
Harmonious order of graphs
✍ Scribed by Andrzej Żak
- Book ID
- 108114155
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 691 KB
- Volume
- 309
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
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## Abstract The hermonious coloring number of the graph __G, HC__(__G__), is the smallest number of colors needed to label the vertices of __G__ such that adjacent vertices received different colors and no two edges are incident with the same color pair. In this paper, we investigate the __HC__‐num
Let K~ ) be the umon of two complete graphs on n vertices which have preosely one vertex in common. Graham and Sloane have shown that K~ ~ is not harmomous for n od:~, /(~,~ is harmonious, and K~62~ is not harmonious. They also conjecture that K~' t,, not h,~rmomous except for n = 4. Here, it Is sho