兰州理工大学学报
蘭州理工大學學報
란주리공대학학보
JOURNAL OF LANZHOU UNIVERSITY OF TECHNOLOGY
2015年
2期
160-163
,共4页
优美图%平衡图%交错图%非连通图
優美圖%平衡圖%交錯圖%非連通圖
우미도%평형도%교착도%비련통도
graceful graph%balanced graph%alternating graph%unconnected graph
讨论非连通图(Cn1⊙r1K1)∪(Cn2⊙r2K1)∪P2的优美性,证明如下结论:设n1,n2,r1,r2是任意自然数,n1≥1,n2≥1,当n1(n+1)=n2(r2+1)或3n1(n+1) =n2(r2+1)时,(C4n1⊙r1 K1)∪(C4n2⊙r2K1) ∪P2是交错图;当n1(r1+1)=n2(r2+1)或(3n1—1)(r1+1)=n2(r2+1)时,非连通图(C4n1-1 ⊙r1K1)∪(C4n2 ⊙r2K1)∪P2是优美的,其中P2是2个顶点的路,Cn是n个顶点的圈,Cm⊙rK1是圈Cm的r-冠.
討論非連通圖(Cn1⊙r1K1)∪(Cn2⊙r2K1)∪P2的優美性,證明如下結論:設n1,n2,r1,r2是任意自然數,n1≥1,n2≥1,噹n1(n+1)=n2(r2+1)或3n1(n+1) =n2(r2+1)時,(C4n1⊙r1 K1)∪(C4n2⊙r2K1) ∪P2是交錯圖;噹n1(r1+1)=n2(r2+1)或(3n1—1)(r1+1)=n2(r2+1)時,非連通圖(C4n1-1 ⊙r1K1)∪(C4n2 ⊙r2K1)∪P2是優美的,其中P2是2箇頂點的路,Cn是n箇頂點的圈,Cm⊙rK1是圈Cm的r-冠.
토론비련통도(Cn1⊙r1K1)∪(Cn2⊙r2K1)∪P2적우미성,증명여하결론:설n1,n2,r1,r2시임의자연수,n1≥1,n2≥1,당n1(n+1)=n2(r2+1)혹3n1(n+1) =n2(r2+1)시,(C4n1⊙r1 K1)∪(C4n2⊙r2K1) ∪P2시교착도;당n1(r1+1)=n2(r2+1)혹(3n1—1)(r1+1)=n2(r2+1)시,비련통도(C4n1-1 ⊙r1K1)∪(C4n2 ⊙r2K1)∪P2시우미적,기중P2시2개정점적로,Cn시n개정점적권,Cm⊙rK1시권Cm적r-관.
