Perfect edge domination and efficient edge domination in graphs
نویسندگان
چکیده
Let G = (V; E) be a /nite and undirected graph without loops and multiple edges. An edge is said to dominate itself and any edge adjacent to it. A subset D of E is called a perfect edge dominating set if every edge of E \ D is dominated by exactly one edge in D and an e cient edge dominating set if every edge of E is dominated by exactly one edge in D. The perfect (e cient) edge domination problem is to /nd a perfect (e cient) edge dominating set of minimum size in G. Suppose that each edge e is associated with a real number w(e) as its weight. Then, the weighted perfect (e cient) edge domination problem is to calculate a perfect (e cient) edge dominating set D such that the weight w(D) of D is minimum, where w(D)= ∑ e∈D w(e). In this paper, we show that the perfect (e cient) edge domination problem is NP-complete on bipartite (planar bipartite) graphs. Moreover, we present linear-time algorithms to solve the weighted perfect (e cient) edge domination problem on generalized series–parallel graphs and chordal graphs. ? 2002 Elsevier Science B.V. All rights reserved.
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ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 119 شماره
صفحات -
تاریخ انتشار 2002