We investigate the dominating-c-color number,, of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result a...We investigate the dominating-c-color number,, of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].展开更多
Diacetates 1 and N-[(1-benzotriazol-l-yl)alkyl]amides 2, both masked forms of aldehydes, could undergo deprotection and condensation with cycloalkanones in a one-pot procedure promoted by samarium(III) iodide (SmI3) ...Diacetates 1 and N-[(1-benzotriazol-l-yl)alkyl]amides 2, both masked forms of aldehydes, could undergo deprotection and condensation with cycloalkanones in a one-pot procedure promoted by samarium(III) iodide (SmI3) to afford α,α'-bis(substituted benzylidene) cycloalkanones in good yields.展开更多
To enumerate isomers of the fluxional molecules, some theorems for maturity and the integer-valued characters of finite groups were introduced by S. Fujita and first author. The full non-rigid group of hexamethylethan...To enumerate isomers of the fluxional molecules, some theorems for maturity and the integer-valued characters of finite groups were introduced by S. Fujita and first author. The full non-rigid group of hexamethylethane is the semi-direct product of the direct products of six copies of the cyclic group Z3 by the dihedral group of order 12 (see, Asian J. Chem. (2010) 22 (3), 1966-1972). In this paper, we continue our study on finite groups (see Int. J. Theo. Physics, Group Theory, and Nonlinear Optics (2013), 17) and all the integer-valued characters of the above molecule are successfully derived.展开更多
文摘We investigate the dominating-c-color number,, of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].
文摘Diacetates 1 and N-[(1-benzotriazol-l-yl)alkyl]amides 2, both masked forms of aldehydes, could undergo deprotection and condensation with cycloalkanones in a one-pot procedure promoted by samarium(III) iodide (SmI3) to afford α,α'-bis(substituted benzylidene) cycloalkanones in good yields.
文摘To enumerate isomers of the fluxional molecules, some theorems for maturity and the integer-valued characters of finite groups were introduced by S. Fujita and first author. The full non-rigid group of hexamethylethane is the semi-direct product of the direct products of six copies of the cyclic group Z3 by the dihedral group of order 12 (see, Asian J. Chem. (2010) 22 (3), 1966-1972). In this paper, we continue our study on finite groups (see Int. J. Theo. Physics, Group Theory, and Nonlinear Optics (2013), 17) and all the integer-valued characters of the above molecule are successfully derived.
