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 (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, (G) (H) (G H), and Clark and Suen (2000) proved that (G) (H) 2 (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 A 1 through A n .
['Keerti Choudhary', 'Susan Margulies', 'Illya V. Hicks']
A Note on Total and Paired Domination of Cartesian Product Graphs