文章摘要
赵科,李敬文,魏众德.优雅图猜想[J].,2018,58(6):641-648
优雅图猜想
Conjecture of elegant graph
  
DOI:10.7511/dllgxb201806013
中文关键词: 优雅标号  优雅图  非优雅图  优雅空间  优雅图猜想
英文关键词: elegant labeling  elegant graphs  non-elegant graphs  elegant spaces  elegant graphs conjectures
基金项目:国家自然科学基金资助项目(11461038,61163010).
作者单位
赵科,李敬文,魏众德  
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中文摘要:
      对于图G(p,q),如果存在一个单射f:V(G)→[0,1,2,…,q],使得f(E(G))={f(uv)=(f(u)+f(v))mod(q+1)|uv∈E(G)}=[1,…,q],则称图G为优雅图.采用剪枝与预判函数相结合的方式,设计了递归回溯算法,对9个点内的所有简单连通图进行了优雅性验证,得到9个点内所有优雅图和非优雅图.根据实验结果,验证了当3≤p≤9时,所有的树图、单圈图几乎都是优雅的,证明了当3≤q≤9且q≠1(mod 4)时,图G(p,q)是优雅的.最后给出猜想:绝大多数的图是优雅的.
英文摘要:
      For graph G(p,q), if there exists an injective function f:V(G)→[0,1,2,…,q], such that f(E(G))={f(uv)=(f(u)+f(v))mod (q+1)|uv∈E(G)}=[1,…,q], the graph G is called an elegant graph. A combination of pruning and predictive function is used to design a recursive backtracking algorithm. The elegance of all the simple connected graphs in 9 points is verified, and all elegant and non-elegant graphs are obtained. According to the experimental results, it is verified that when 3≤p≤9, all tree graphs and unicyclic graphs are almost elegant, which proves that when 3≤q≤9 and q≠1(mod 4), the graph G(p,q)is elegant. Finally, the conjecture that the majority of the graphs are elegant is given.
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