Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph...Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph K3 and cycle Cm.First we have the Lemma 2,if uv ∈ E(G),G is Cordial,we add 4 vertices x,y,z,w in sequence to the edge uv,obtain a new graph denoted by G*,then G* is still Cordial,by this lemma,we consider four cases on the union of 3-regular connected graph R3,and for every case we distinguish four subcases on the cycle Cm.展开更多
将文献[2](Shee S C,Ho Y S.The Cordiality of One-point Union of n-copies of a Graph.Discrete Math,1993,117:225-243)的结果推广到一般的圈的一点联,即粘连的圈的个数是任意的且每个圈的顶点数也是任意的情况,并给出了此类一点联...将文献[2](Shee S C,Ho Y S.The Cordiality of One-point Union of n-copies of a Graph.Discrete Math,1993,117:225-243)的结果推广到一般的圈的一点联,即粘连的圈的个数是任意的且每个圈的顶点数也是任意的情况,并给出了此类一点联的Cordial性的分析证明.展开更多
利用文献[5](Seoud M,Abdel Maqsoud A E I,Sheehan J.Harmonious Graphs.Util Math,1995,47:225-233.)中的引理1,研究了Pm1×Pn1与Pm2×Pn2的连接和Pm×Pn与Ck的连接的Cordial性,得到当m1,m2,n1,n2≥2时,(Pm1×Pn1)∨(...利用文献[5](Seoud M,Abdel Maqsoud A E I,Sheehan J.Harmonious Graphs.Util Math,1995,47:225-233.)中的引理1,研究了Pm1×Pn1与Pm2×Pn2的连接和Pm×Pn与Ck的连接的Cordial性,得到当m1,m2,n1,n2≥2时,(Pm1×Pn1)∨(Pm2×Pn2)均为Cordial图;当m,n≥2时,(Pm×Pn)∨Ck是Cordial图的充要条件.展开更多
给出了路Pm、圈Cn、扇Fp和轮Wq4种图之间和的Cordial性,所得结果扩展了文献[1](Gallian J A.ADynamic Survey of Graph Labellings of Graphs.Electronic Journal of Combinatorics,2005(5):DS6)的研究工作.
研究2-正则图G的cordial性,证明了2-正则图G是cordial图的充要条件为|G|≠2(mod4);取消了文献[1](Cahit I.On cordial and 3-equitbale labeling of graphs.Utilitas Math,1990,37:189-198)中具有4n+2条边的Euler图不是cordial图这一定...研究2-正则图G的cordial性,证明了2-正则图G是cordial图的充要条件为|G|≠2(mod4);取消了文献[1](Cahit I.On cordial and 3-equitbale labeling of graphs.Utilitas Math,1990,37:189-198)中具有4n+2条边的Euler图不是cordial图这一定理中连通性条件,证明了具有4n+2条边并且顶点的度都是偶数的图不是cordial图.展开更多
基于图的cordial标号,给出了3个引理:cordial图G联结上一个P2×Pn图得到的新图仍是cordial图;每个图P2k+1×P2l都有2个cordial标号;至少有1个图边数为偶数或者边数都为奇数但0边之和等于1边之和的2个cordial图的并为cordial图....基于图的cordial标号,给出了3个引理:cordial图G联结上一个P2×Pn图得到的新图仍是cordial图;每个图P2k+1×P2l都有2个cordial标号;至少有1个图边数为偶数或者边数都为奇数但0边之和等于1边之和的2个cordial图的并为cordial图.最后运用这3个引理证明了from i=1 to r (P_(mi)×P_(ni)为cordial图.展开更多
将文献[5](Shee S C,Ho YS.The Cordiality of the Path-union ofnCopies of a Graph.Discrete Math,1996,151:221-229.)的结果推广到Tn-union的情形,且不要求每个节点的图形必须相同.并给出了任意圈和扇Tn-union的Cordial性的分析和证明.
文摘Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph K3 and cycle Cm.First we have the Lemma 2,if uv ∈ E(G),G is Cordial,we add 4 vertices x,y,z,w in sequence to the edge uv,obtain a new graph denoted by G*,then G* is still Cordial,by this lemma,we consider four cases on the union of 3-regular connected graph R3,and for every case we distinguish four subcases on the cycle Cm.
文摘将文献[2](Shee S C,Ho Y S.The Cordiality of One-point Union of n-copies of a Graph.Discrete Math,1993,117:225-243)的结果推广到一般的圈的一点联,即粘连的圈的个数是任意的且每个圈的顶点数也是任意的情况,并给出了此类一点联的Cordial性的分析证明.
文摘利用文献[5](Seoud M,Abdel Maqsoud A E I,Sheehan J.Harmonious Graphs.Util Math,1995,47:225-233.)中的引理1,研究了Pm1×Pn1与Pm2×Pn2的连接和Pm×Pn与Ck的连接的Cordial性,得到当m1,m2,n1,n2≥2时,(Pm1×Pn1)∨(Pm2×Pn2)均为Cordial图;当m,n≥2时,(Pm×Pn)∨Ck是Cordial图的充要条件.
文摘给出了路Pm、圈Cn、扇Fp和轮Wq4种图之间和的Cordial性,所得结果扩展了文献[1](Gallian J A.ADynamic Survey of Graph Labellings of Graphs.Electronic Journal of Combinatorics,2005(5):DS6)的研究工作.
文摘研究2-正则图G的cordial性,证明了2-正则图G是cordial图的充要条件为|G|≠2(mod4);取消了文献[1](Cahit I.On cordial and 3-equitbale labeling of graphs.Utilitas Math,1990,37:189-198)中具有4n+2条边的Euler图不是cordial图这一定理中连通性条件,证明了具有4n+2条边并且顶点的度都是偶数的图不是cordial图.
文摘基于图的cordial标号,给出了3个引理:cordial图G联结上一个P2×Pn图得到的新图仍是cordial图;每个图P2k+1×P2l都有2个cordial标号;至少有1个图边数为偶数或者边数都为奇数但0边之和等于1边之和的2个cordial图的并为cordial图.最后运用这3个引理证明了from i=1 to r (P_(mi)×P_(ni)为cordial图.
文摘将文献[5](Shee S C,Ho YS.The Cordiality of the Path-union ofnCopies of a Graph.Discrete Math,1996,151:221-229.)的结果推广到Tn-union的情形,且不要求每个节点的图形必须相同.并给出了任意圈和扇Tn-union的Cordial性的分析和证明.
