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Title: Equality in Vizing’s conjecture fixing one factor of the Cartesian product.
Authors: Nazzal, Khalida
Khamis, Suheir
Keywords: Domination number, Cartesian product, Vizing’s conjecture
Domination number, Cartesian product, Vizing’s conjecture.
Issue Date: 30-Jul-2010
Publisher: Ars combinatoria
Citation: Ars combinatoria Vol. (96) July, 2010. 375–384.
Series/Report no.: (96);375–384.
Abstract: In this paper, we investigate the existence of nontrivial solutions for the equation γ(G□H) = γ(G) γ(H) fixing one factor. For the complete bipartite graphs Km,n; we characterize all nontrivial solutions when m = 2, n ≥ 3and prove the nonexistence of solutions when m, n ≥ 3. In addition, it is proved that the above equation has no nontrivial solution if H is one of the graphs obtained from Cn, the cycle of length n, either by adding a vertex and one pendant edge joining this vertex to any v V(Cn), or by adding one chord joining two alternating vertices of Cn (17) (PDF) Equality in Vizing's Conjecture Fixing One Factor of the Cartesian Product. Available from:'s_Conjecture_Fixing_One_Factor_of_the_Cartesian_Product [accessed Jan 23 2019].
Description: Article
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