This paper gives new sufficient conditions for a connected graph to be Hamiltonian and Hamiltonian connected by independence number and neighbourhood intersections of three independent vertices with distance 2.
This paper deals with the problem of labeling the vertices, edges and faces of a plane graph. A weight of a face is the sum of the label of a face and the labels of the vertices and edges surrounding that face. In a s...This paper deals with the problem of labeling the vertices, edges and faces of a plane graph. A weight of a face is the sum of the label of a face and the labels of the vertices and edges surrounding that face. In a super d-antimagic labeling the vertices receive the smallest labels and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s appearing in the graph. The paper examines the existence of such labelings for plane graphs containing a special Hamilton path.展开更多
In the present paper we discuss some properties of book presentation of spatial graphs, and prove that the book presentation of minimum sheets of a complete graph K2m with even vertices is unique up to sheet translati...In the present paper we discuss some properties of book presentation of spatial graphs, and prove that the book presentation of minimum sheets of a complete graph K2m with even vertices is unique up to sheet translation and ambient isotopy. We also show this is true for K7.展开更多
文摘This paper gives new sufficient conditions for a connected graph to be Hamiltonian and Hamiltonian connected by independence number and neighbourhood intersections of three independent vertices with distance 2.
文摘This paper deals with the problem of labeling the vertices, edges and faces of a plane graph. A weight of a face is the sum of the label of a face and the labels of the vertices and edges surrounding that face. In a super d-antimagic labeling the vertices receive the smallest labels and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s appearing in the graph. The paper examines the existence of such labelings for plane graphs containing a special Hamilton path.
基金Foundation item： the National Natural Science Foundation of China （No. 15071034） the Foundation of Dalian University of Technology （No. 893322）.
文摘In the present paper we discuss some properties of book presentation of spatial graphs, and prove that the book presentation of minimum sheets of a complete graph K2m with even vertices is unique up to sheet translation and ambient isotopy. We also show this is true for K7.
