摘要
讨论非连通图(P1∨Pn)∪Gr和(P1∨Pn)∪(P3∨■r)及Wn∪St(m)的优美性,证明了如下结论:设n,m为任意正整数,s=[n/2],r=s-1,Gr是任意具有r条边的优美图,则当n≥4时,非连通图(P1∨Pn)∪Gr和(P1∨Pn)∪(P3∨■r)是优美图;当n≥3,m≥s时,非连通图Wn∪St(m)是优美图.其中,Pn是n个顶点的路,Kn是n个顶点的完全图,K-n是Kn的补图,G1∨G2是图G1与G2的联图,Wn是n+1个顶点的轮图,St(m)是m+1个顶点的星形树.
The present paper deals with the gracefulness of three kinds of unconnected graphs ( Pi ∨ P.) L/Gr, (P1∨Pn)∪ (P3∨ Kr) and Wn ∪ St( m), and proves the following results: for positive integers n and m, let s = [ n/2 ], r = s - 1, Gr be a graceful graph with r-edges, if n ≥4, then the unconnected graphs ( PI V P.) U Gr and (P1∨ Pn ) ∪ ( P3 ∨ Kr ) are both graceful graphs ; if n ≤ 3 and m ≥s, then the unconnected graph Wn∪St(m) is a graceful graph, where P. is an n-vertex path, K. is an n-vertex complete graph, K. is the complement of graph Kn, graph G1 ∨ G2 is the join graph of GI and G2, Wn is an ( n + 1 ) -vertex wheel graph and St(m) is an ( m + 1 ) -vertex star tree.
出处
《吉林大学学报(理学版)》
CAS
CSCD
北大核心
2007年第4期539-543,共5页
Journal of Jilin University:Science Edition
关键词
优美图
优美标号
非连通图
graceful graph
graceful label
unconnected graph