In the present, the authors investigate a new type of separation axioms, which they call it w s-regular. The authors obtained some of its basic properties and its characterizations. Also, the authors notice that the a...In the present, the authors investigate a new type of separation axioms, which they call it w s-regular. The authors obtained some of its basic properties and its characterizations. Also, the authors notice that the axiom of tO s-regularity is weaker than the regularity, stronger than s-regularity and it is independent of w -regularity. However, the authors showed that the w s-regularity and regularity are identical on the class of all locally countable spaces, while the concepts ofw s-regularity and s-regularity are same on the class of anti-locally countable spaces：; furthermore, they proved that the three concepts w s-regularity, s-regularity and w s-regularity are same on the class of extremally disconnected spaces. The authors characterized w s-regular Trspaces by g-open sets, and they proved that the w s-regularity is an open hereditary property and it is also a topologizal property. The w s-closure of subsets of topological spaces are investigated and characterized. The authors used the concepts w s-closure to obtain some characterizations of the w s-regular spaces. Behind those, the authors obtained some properties and characterizations of w -semi open sets.展开更多
A graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. An infinite family of cubic 1-regular graphs was constructed in [7] as cyclic coverings of the three-dimensional Hypercube, and a...A graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. An infinite family of cubic 1-regular graphs was constructed in [7] as cyclic coverings of the three-dimensional Hypercube, and a classification of all s-regular cyclic coverings of the complete bipartite graph of order 6 was given in [8] for each s ≥ 1, whose fibre-preserving automorphism subgroups act arc-transitively. In this paper, the authors classify all s-regular dihedral coverings of the complete graph of order 4 for each s ≥ 1, whose fibre-preserving automorphism subgroups act arc-transitively. As a result, a new infinite family of cubic 1-regular graphs is constructed.展开更多
文摘In the present, the authors investigate a new type of separation axioms, which they call it w s-regular. The authors obtained some of its basic properties and its characterizations. Also, the authors notice that the axiom of tO s-regularity is weaker than the regularity, stronger than s-regularity and it is independent of w -regularity. However, the authors showed that the w s-regularity and regularity are identical on the class of all locally countable spaces, while the concepts ofw s-regularity and s-regularity are same on the class of anti-locally countable spaces：; furthermore, they proved that the three concepts w s-regularity, s-regularity and w s-regularity are same on the class of extremally disconnected spaces. The authors characterized w s-regular Trspaces by g-open sets, and they proved that the w s-regularity is an open hereditary property and it is also a topologizal property. The w s-closure of subsets of topological spaces are investigated and characterized. The authors used the concepts w s-closure to obtain some characterizations of the w s-regular spaces. Behind those, the authors obtained some properties and characterizations of w -semi open sets.
基金the Excellent Young Teachers Program of the Ministry of Education of Chinathe National Natural Science Foundation of China+1 种基金 the Scientific Research Foundation for the Returned Overseas Chinese Scholars the Ministry of Education of China and the Com2MaC-KOSEF in Korea.
文摘A graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. An infinite family of cubic 1-regular graphs was constructed in [7] as cyclic coverings of the three-dimensional Hypercube, and a classification of all s-regular cyclic coverings of the complete bipartite graph of order 6 was given in [8] for each s ≥ 1, whose fibre-preserving automorphism subgroups act arc-transitively. In this paper, the authors classify all s-regular dihedral coverings of the complete graph of order 4 for each s ≥ 1, whose fibre-preserving automorphism subgroups act arc-transitively. As a result, a new infinite family of cubic 1-regular graphs is constructed.
