A locally semicomplete digraph is a digraph D=(V,A) satisfying the following condi-tion for every vertex x∈V the D[O(x)] and D[I(x)] are semicomplete digraphs. In this paper,we get some properties of cycles and deter...A locally semicomplete digraph is a digraph D=(V,A) satisfying the following condi-tion for every vertex x∈V the D[O(x)] and D[I(x)] are semicomplete digraphs. In this paper,we get some properties of cycles and determine the exponent set of primitive locally semicompleted digraphs.展开更多
A subset of S of the vertex set of a graph G is called acyclic if the subgraph it induces in G contains no cycles. S is called an acyclic dominating set of G if it is both acyclic and dominating. The minimum cardinali...A subset of S of the vertex set of a graph G is called acyclic if the subgraph it induces in G contains no cycles. S is called an acyclic dominating set of G if it is both acyclic and dominating. The minimum cardinality of an acyclic dominating set, denoted by γα(G), is called the acyclic domination number of G. S. M. Hedetniemi et al. on 2000 introduced the concept of acyclic domination and posed the following open problem: Is γα(G) ≤ δ(G) for any graph whose diameter is two? In this paper, we give a counterexample which disproves the problem.展开更多
In this paper, we generate all nonisomorphic tournaments of order at mostnine, all nonisomorphic almost regular tournaments of order 10 and all nonisomorphic regulartournaments of order 11. For each of these tournamen...In this paper, we generate all nonisomorphic tournaments of order at mostnine, all nonisomorphic almost regular tournaments of order 10 and all nonisomorphic regulartournaments of order 11. For each of these tournaments, we have given its score-list, connectivity,diameter, the minimal number of feedbacks, automorphisms and spectra. Moreover, we have verified thewell-known Kelly's Conjecture for n = 2k + 1 ≤ 11. And we also determine the n-universaltournaments for n ≤ 6. However, several related results are given and some related open problemsare raised.展开更多
文摘A locally semicomplete digraph is a digraph D=(V,A) satisfying the following condi-tion for every vertex x∈V the D[O(x)] and D[I(x)] are semicomplete digraphs. In this paper,we get some properties of cycles and determine the exponent set of primitive locally semicompleted digraphs.
基金This research is supported by the National Natural Science Foundation of ChinaThis project is supported by Nanjing University Talent Development Foundation.
文摘A subset of S of the vertex set of a graph G is called acyclic if the subgraph it induces in G contains no cycles. S is called an acyclic dominating set of G if it is both acyclic and dominating. The minimum cardinality of an acyclic dominating set, denoted by γα(G), is called the acyclic domination number of G. S. M. Hedetniemi et al. on 2000 introduced the concept of acyclic domination and posed the following open problem: Is γα(G) ≤ δ(G) for any graph whose diameter is two? In this paper, we give a counterexample which disproves the problem.
文摘In this paper, we generate all nonisomorphic tournaments of order at mostnine, all nonisomorphic almost regular tournaments of order 10 and all nonisomorphic regulartournaments of order 11. For each of these tournaments, we have given its score-list, connectivity,diameter, the minimal number of feedbacks, automorphisms and spectra. Moreover, we have verified thewell-known Kelly's Conjecture for n = 2k + 1 ≤ 11. And we also determine the n-universaltournaments for n ≤ 6. However, several related results are given and some related open problemsare raised.
