This paper deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and the labels of the vertices and edges surrounding that face add up to a weight of ...This paper deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and the labels of the vertices and edges surrounding that face add up to a weight of that face, and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s that appears in the graph. The paper examines the existence of such labelings for disjoint union of plane graphs.展开更多
In this paper, Betti numbers are evaluated for several classes of graphs whose complements are bipartite graphs. Relations are established for the general case, and counting formulae are given in several particular ca...In this paper, Betti numbers are evaluated for several classes of graphs whose complements are bipartite graphs. Relations are established for the general case, and counting formulae are given in several particular cases, including the union of several mutually disjoint complete graphs.展开更多
文摘This paper deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and the labels of the vertices and edges surrounding that face add up to a weight of that face, and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s that appears in the graph. The paper examines the existence of such labelings for disjoint union of plane graphs.
基金This research was supported by the National Natural Science Foundation of China （Grant No. 11271250）.
文摘In this paper, Betti numbers are evaluated for several classes of graphs whose complements are bipartite graphs. Relations are established for the general case, and counting formulae are given in several particular cases, including the union of several mutually disjoint complete graphs.
