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
In this paper,the authors determine maximal connected automorphism group of the Lie transformation group T（D（VN,F））,which acting on the normal Siegel domain D（VN,F）is simple and transitive,and prove that the max...In this paper,the authors determine maximal connected automorphism group of the Lie transformation group T（D（VN,F））,which acting on the normal Siegel domain D（VN,F）is simple and transitive,and prove that the maximal connected automorphism group of T（D（VN,F））is its maximal connected inner automorphism group.展开更多
Let n,m,k be positive integers and b_(m,k) be the number of representations of n as n = m^(a_0) + m^(a_1) + ··· + m^(a_j) with 0 ≤ a_0 ≤ a_1 ≤···≤ a_j < k.In this note,we obtain so...Let n,m,k be positive integers and b_(m,k) be the number of representations of n as n = m^(a_0) + m^(a_1) + ··· + m^(a_j) with 0 ≤ a_0 ≤ a_1 ≤···≤ a_j < k.In this note,we obtain some congruences and distribution properties of b_(m,k).展开更多
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.
基金Supported by the National Science Foundation of China（11047030） Supported by the Natural Science Foundation of Henan Provincial Education Department（2010B11003） Supported by the Natural Science Foundation of Henan University（2009YBZR025）
文摘In this paper,the authors determine maximal connected automorphism group of the Lie transformation group T（D（VN,F））,which acting on the normal Siegel domain D（VN,F）is simple and transitive,and prove that the maximal connected automorphism group of T（D（VN,F））is its maximal connected inner automorphism group.
基金Foundation item： Supported by the National Natural Science Foundation of China（11101123） Supported by the Natural Science Foundation of Education Department of Henan Province（2009A110001）
文摘Let n,m,k be positive integers and b_(m,k) be the number of representations of n as n = m^(a_0) + m^(a_1) + ··· + m^(a_j) with 0 ≤ a_0 ≤ a_1 ≤···≤ a_j < k.In this note,we obtain some congruences and distribution properties of b_(m,k).
