论文信息 - On a Vizing-like conjecture for direct product graphs

On a Vizing-like conjecture for direct product graphs

Abstract Let γ ( G ) be the domination number of a graph G , and let G × H be the direct product of graphs G and H . It is shown that for any k ⩾ 0 there exists a graph G such that γ ( G × G ) ⩽ γ ( G ) 2 − k . This in particular disproves a conjecture from [5].

Sandi Klavzar | Blaz Zmazek

[1] Michael S. Jacobson,et al. On the domination of the products of graphs II: Trees , 1986, J. Graph Theory.

[2] David C. Fisher. Domination, Fractional Domination, 2-Packing, and Graph Products , 1994, SIAM J. Discret. Math..

[3] V. G. Vizing. The cartesian product of graphs , 1963 .

[4] Douglas F. Rall,et al. Associative graph products and their independence, domination and coloring numbers , 1996, Discuss. Math. Graph Theory.

[5] Norbert Seifter,et al. Dominating Cartesian Products of Cycles , 1995, Discret. Appl. Math..

[6] Sylvain Gravier,et al. On the domination number of cross products of graphs , 1995, Discret. Math..

[7] W. Edwin Clark,et al. The domination numbers of the 5 × n and 6 × n grid graphs , 1993, J. Graph Theory.