A Note on Total and Paired Domination of Cartesian Product Graphs
نویسندگان
چکیده
A dominating set D for a graph G is a subset of V (G) such that any vertex not in D has at least one neighbor in D. The domination number γ(G) is the size of a minimum dominating set in G. Vizing’s conjecture from 1968 states that for the Cartesian product of graphs G and H, γ(G)γ(H) ≤ γ(G H), and Clark and Suen (2000) proved that γ(G)γ(H) ≤ 2γ(G H). In this paper, we modify the approach of Clark and Suen to prove a variety of similar bounds related to total and paired domination, and also extend these bounds to the n-Cartesian product of graphs A1 through An.
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عنوان ژورنال:
- Electr. J. Comb.
دوره 20 شماره
صفحات -
تاریخ انتشار 2013