Partitioning the vertex set of G to make G ☐ H an efficient open domination graph
نویسندگان
چکیده
A graph is an efficient open domination graph if there exists a subset of vertices whose open neighborhoods partition its vertex set. We characterize those graphs G for which the Cartesian product G H is an efficient open domination graph when H is a complete graph of order at least 3 or a complete bipartite graph. The characterization is based on the existence of a certain type of weak partition of V (G). For the class of trees when H is complete of order at least 3, the characterization is constructive. In addition, a special type of efficient open domination graph is characterized among Cartesian products G H when H is a 5-cycle or a 4-cycle.
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عنوان ژورنال:
- Discrete Mathematics & Theoretical Computer Science
دوره 18 شماره
صفحات -
تاریخ انتشار 2016