In this paper we give a formula for enumerating the equivalent classes of orderly labeled Hamiltonian graphs under group D. and two algorithms for constructing these equivalent classes and all nonisomorphic Hamiltonia...In this paper we give a formula for enumerating the equivalent classes of orderly labeled Hamiltonian graphs under group D. and two algorithms for constructing these equivalent classes and all nonisomorphic Hamiltonian graphs. Some computational results obtained by microcomputers are listed.展开更多
Catalan number is an important class of combinatorial numbers. The maximal outerplanar graphs are important in graph theory. In this paper some formulas to enumerate the numbers of maximal outerplanar graphs by means ...Catalan number is an important class of combinatorial numbers. The maximal outerplanar graphs are important in graph theory. In this paper some formulas to enumerate the numbers of maximal outerplanar graphs by means of the compressing graph and group theory method are given first. Then the relationships between Catalan numbers and the numbers of labeled and unlabeled maximal outerplanar graphs are presented. The computed results verified these formulas.展开更多
Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. In this article, the maximum size of an acyclic hypergraph is determined and the number of maximum γ-uniform ac...Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. In this article, the maximum size of an acyclic hypergraph is determined and the number of maximum γ-uniform acyclic hypergraphs of order n is shown to be展开更多
基金Project supported by National Natural Foundation of China
文摘In this paper we give a formula for enumerating the equivalent classes of orderly labeled Hamiltonian graphs under group D. and two algorithms for constructing these equivalent classes and all nonisomorphic Hamiltonian graphs. Some computational results obtained by microcomputers are listed.
文摘Catalan number is an important class of combinatorial numbers. The maximal outerplanar graphs are important in graph theory. In this paper some formulas to enumerate the numbers of maximal outerplanar graphs by means of the compressing graph and group theory method are given first. Then the relationships between Catalan numbers and the numbers of labeled and unlabeled maximal outerplanar graphs are presented. The computed results verified these formulas.
基金Supported by the National Natural Science Foundation of China (No.19831080)
文摘Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. In this article, the maximum size of an acyclic hypergraph is determined and the number of maximum γ-uniform acyclic hypergraphs of order n is shown to be
