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
A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vert...A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.展开更多
The induced matching cover number of a graph G without isolated vertices, denoted by imc(G),is the minimum integer k such that G has k induced matchings {M1,M2,···,Mk}such that,V(M1)∪V(M2)∪··...The induced matching cover number of a graph G without isolated vertices, denoted by imc(G),is the minimum integer k such that G has k induced matchings {M1,M2,···,Mk}such that,V(M1)∪V(M2)∪···∪V(Mk)covers V(G).This paper shows that,if G is a 3-regular claw-free graph,then imc(G)∈{2,3}.展开更多
It is well-known that the Petersen graph is nonhamiltonian.A very short proof for this result was presented in[2]due to D.B.West.In this note,by extending the proof technique in[2],we briefly show that the girth of ev...It is well-known that the Petersen graph is nonhamiltonian.A very short proof for this result was presented in[2]due to D.B.West.In this note,by extending the proof technique in[2],we briefly show that the girth of every 3-regular hamiltonian graph on n≥10 vertices is at most(n+4)/3.展开更多
This artical concerns the C_(loc)^(1,α)-regularity of weak solutions u to the degenerate subelliptic p-Laplacian equationΔ_(H,p)u(x)=∑_(i=1)^(6)X_(i)^(*)(|∇_(H)u|^(p-2)X_(i)u)=0,where H is the orthogonal complement...This artical concerns the C_(loc)^(1,α)-regularity of weak solutions u to the degenerate subelliptic p-Laplacian equationΔ_(H,p)u(x)=∑_(i=1)^(6)X_(i)^(*)(|∇_(H)u|^(p-2)X_(i)u)=0,where H is the orthogonal complement of a Cartan subalgebra in SU(3)with the orthonormal basis composed of the vector fields X_(1),...,X_(6).When 1<p<2,we prove that ∇_(H)u∈C_(loc)^(α).展开更多
Explicit Stationary Distribution of the(L,1)-reflecting Random Walk on the Half Line Wen Ming HONG Ke ZHOU Yi Qiang Q.ZHAO Abstract In this paper,we consider the(L,1)state-dependent reflecting random walk(RW)on the ha...Explicit Stationary Distribution of the(L,1)-reflecting Random Walk on the Half Line Wen Ming HONG Ke ZHOU Yi Qiang Q.ZHAO Abstract In this paper,we consider the(L,1)state-dependent reflecting random walk(RW)on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for(positive)recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper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.
文摘A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.
基金Supported by the National Natural Science Foundation of China（10771179）
文摘The induced matching cover number of a graph G without isolated vertices, denoted by imc(G),is the minimum integer k such that G has k induced matchings {M1,M2,···,Mk}such that,V(M1)∪V(M2)∪···∪V(Mk)covers V(G).This paper shows that,if G is a 3-regular claw-free graph,then imc(G)∈{2,3}.
基金Supported by National Natural Science Foundation of China(Grant No.12071442)the Fundamental Research Funds for the Central Universities under(Grant No.020314380035)。
文摘It is well-known that the Petersen graph is nonhamiltonian.A very short proof for this result was presented in[2]due to D.B.West.In this note,by extending the proof technique in[2],we briefly show that the girth of every 3-regular hamiltonian graph on n≥10 vertices is at most(n+4)/3.
基金supported by the National Natural Science Foundation of China(Nos.12025102,11871088).
文摘This artical concerns the C_(loc)^(1,α)-regularity of weak solutions u to the degenerate subelliptic p-Laplacian equationΔ_(H,p)u(x)=∑_(i=1)^(6)X_(i)^(*)(|∇_(H)u|^(p-2)X_(i)u)=0,where H is the orthogonal complement of a Cartan subalgebra in SU(3)with the orthonormal basis composed of the vector fields X_(1),...,X_(6).When 1<p<2,we prove that ∇_(H)u∈C_(loc)^(α).
文摘Explicit Stationary Distribution of the(L,1)-reflecting Random Walk on the Half Line Wen Ming HONG Ke ZHOU Yi Qiang Q.ZHAO Abstract In this paper,we consider the(L,1)state-dependent reflecting random walk(RW)on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for(positive)recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper
