One conjecture of bubble-sort graphs
β Scribed by Hai-zhong Shi; Pan-feng Niu; Jian-bo Lu
- Book ID
- 108154782
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 187 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0020-0190
No coin nor oath required. For personal study only.
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## Abstract An __n__βdimensional bubbleβsort graph is regular and symmetric. It has __n__! nodes and (__n__β1)__n__!/2 edges while its connectivity and diameter are __n__β1 and __n__(__n__β1)/2, respectively. Bubbleβsort graphs are attracting attention because of their simple, symmetric, and recurs
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