A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck（G） of G is the minimum cardinality taken ove...A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck（G） of G is the minimum cardinality taken over all minimal k-connected dominating sets of G.In this paper,we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers.展开更多
Each vertex of a graph G = （V, E） is said to dominate every vertex in its closed neighborhood. A set S C V is a double dominating set for G if each vertex in V is dominated by at least two vertices in S. The smalles...Each vertex of a graph G = （V, E） is said to dominate every vertex in its closed neighborhood. A set S C V is a double dominating set for G if each vertex in V is dominated by at least two vertices in S. The smallest cardinality of a double dominating set is called the double dominating number dd（G）. In this paper, new relationships between dd（G） and other domination parameters are explored and some results of [1] are extended. Furthermore, we give the Nordhaus-Gaddum-type results for double dominating number.展开更多
文摘A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck（G） of G is the minimum cardinality taken over all minimal k-connected dominating sets of G.In this paper,we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers.
基金the National Natural Science Foundation of China (19871036)
文摘Each vertex of a graph G = （V, E） is said to dominate every vertex in its closed neighborhood. A set S C V is a double dominating set for G if each vertex in V is dominated by at least two vertices in S. The smallest cardinality of a double dominating set is called the double dominating number dd（G）. In this paper, new relationships between dd（G） and other domination parameters are explored and some results of [1] are extended. Furthermore, we give the Nordhaus-Gaddum-type results for double dominating number.
