# Erfang Shan

• Discrete Mathematics
• 2008
A set M of edges of a graph G is a matching if no two edges in M are incident to the same vertex. A set S of vertices in G is a total dominating set ofG if every vertex of G is adjacent to some vertex in S. The matching number is the maximum cardinality of a matching of G, while the total domination number of G is the minimum cardinality of a totalâ€¦ (More)
• Discrete Applied Mathematics
• 2009
4 A set S of vertices in a graph H = (V, E) with no isolated vertices is a paired-dominating 5 set of H if every vertex of H is adjacent to at least one vertex in S and if the subgraph 6 induced by S contains a perfect matching. Let G be a permutation graph and Ï€ be its 7 corresponding permutation. In this paper we present an O(mn) time algorithm forâ€¦ (More)
• Theor. Comput. Sci.
• 2006
The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known domination problem in graphs. In 2002, Haynes et al. considered the graph theoretical representation of this problem as a variation of the domination problem. They defined a set S to be a power dominatingâ€¦ (More)
• Discrete Applied Mathematics
• 2004
For a graph G of order n, let (G), 2(G) and t(G) be the domination, double domination and total domination numbers of G, respectively. The minimum degree of the vertices of G is denoted by (G) and the maximum degree by (G). In this note we prove a conjecture due to Harary and Haynes saying that if a graph G has (G); ( 9 G)Â¿ 4, then 2(G) + 2( 9 G)6 nâˆ’ (G) +â€¦ (More)
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• Graphs and Combinatorics
• 2016
A clique is defined as a complete subgraph maximal under inclusion and having at least two vertices. A k-clique-coloring of a graph G is an assignment of k colors to the vertices of G such that no clique of G is monochromatic. BacsÃ³ et al. (SIAM J Discrete Math 17:361â€“376, 2004) noted that the clique-coloring number is unbounded even for the line graphs ofâ€¦ (More)