In 2012, Ponraj et al. defined a concept of k-product cordial labeling as follows: Let f be a map from V(G)to { 0,1,⋯,k−1 }where k is an integer, 1≤k≤| V(G) |. For each edge uvassign the label f(u)f(v)(modk). f is c...In 2012, Ponraj et al. defined a concept of k-product cordial labeling as follows: Let f be a map from V(G)to { 0,1,⋯,k−1 }where k is an integer, 1≤k≤| V(G) |. For each edge uvassign the label f(u)f(v)(modk). f is called a k-product cordial labeling if | vf(i)−vf(j) |≤1, and | ef(i)−ef(j) |≤1, i,j∈{ 0,1,⋯,k−1 }, where vf(x)and ef(x)denote the number of vertices and edges respectively labeled with x (x=0,1,⋯,k−1). Motivated by this concept, we further studied and established that several families of graphs admit k-product cordial labeling. In this paper, we show that the path graphs Pnadmit k-product cordial labeling.展开更多
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
Crude seed gum and their carboxymethyl derivatives from Tamarindus indica and Cassia fistula seeds were developed and characterized to apply as the pharmaceutical disintegrant in fast disintegrating Thai cordial table...Crude seed gum and their carboxymethyl derivatives from Tamarindus indica and Cassia fistula seeds were developed and characterized to apply as the pharmaceutical disintegrant in fast disintegrating Thai cordial tablet. The chemical structure of crude gum was chemically modified via carboxymethylation. Degree of substitution(DS) of carboxymethylated gums was determined. Carboxymethylated gums with minimum and maximum DS values were chosen for further application. IR absorption spectra of gum samples were observed to verify their chemical structure changes. In physical properties, the intrinsic viscosity and swelling property of all gum samples were evaluated. The results showed that carboxymethylated gums had higher intrinsic viscosity than those of crude gum. Moreover, they could swell and be soluble in cold water better than those of crude gums. In conclusion, the modified gums from both plants could provide higher hardness and be better used than that crude gums for fast disintegrating Thai cordial tablet. However, this is a preliminary assessment to expressing pharmaceutical application possibility of these gums as disintegrants, diluents and drug release controlling agents.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
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.
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 (Pmi×Pni为cordial图.展开更多
摘要In 2012, Ponraj et al. defined a concept of k-product cordial labeling as follows: Let f be a map from V(G)to { 0,1,⋯,k−1 }where k is an integer, 1≤k≤| V(G) |. For each edge uvassign the label f(u)f(v)(modk). f is called a k-product cordial labeling if | vf(i)−vf(j) |≤1, and | ef(i)−ef(j) |≤1, i,j∈{ 0,1,⋯,k−1 }, where vf(x)and ef(x)denote the number of vertices and edges respectively labeled with x (x=0,1,⋯,k−1). Motivated by this concept, we further studied and established that several families of graphs admit k-product cordial labeling. In this paper, we show that the path graphs Pnadmit k-product cordial labeling.
摘要研究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.
基金Higher Education Research Promotion-National Research Universities (HERP-NRU) for financial supporting under grant no. 2558A10862016
摘要Crude seed gum and their carboxymethyl derivatives from Tamarindus indica and Cassia fistula seeds were developed and characterized to apply as the pharmaceutical disintegrant in fast disintegrating Thai cordial tablet. The chemical structure of crude gum was chemically modified via carboxymethylation. Degree of substitution(DS) of carboxymethylated gums was determined. Carboxymethylated gums with minimum and maximum DS values were chosen for further application. IR absorption spectra of gum samples were observed to verify their chemical structure changes. In physical properties, the intrinsic viscosity and swelling property of all gum samples were evaluated. The results showed that carboxymethylated gums had higher intrinsic viscosity than those of crude gum. Moreover, they could swell and be soluble in cold water better than those of crude gums. In conclusion, the modified gums from both plants could provide higher hardness and be better used than that crude gums for fast disintegrating Thai cordial tablet. However, this is a preliminary assessment to expressing pharmaceutical application possibility of these gums as disintegrants, diluents and drug release controlling agents.
摘要将文献[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.
摘要给出了路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.
摘要基于图的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 (Pmi×Pni为cordial图.