论文信息 - Distinguishing Cartesian Products of Countable Graphs

Distinguishing Cartesian Products of Countable Graphs

Abstract The distinguishing number D(G) of a graph G is the minimum number of colors needed to color the vertices of G such that the coloring is preserved only by the trivial automorphism. In this paper we improve results about the distinguishing number of Cartesian products of finite and infinite graphs by removing restrictions to prime or relatively prime factors.

Ehsan Estaji | Wilfried Imrich | Thomas W. Tucker | Monika Pilsniak | Rafal Kalinowski

[1] Thomas W. Tucker,et al. Distinguishability of Infinite Groups and Graphs , 2012, Electron. J. Comb..

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

[3] Wilfried Imrich,et al. Distinguishing Cartesian powers of graphs , 2006, J. Graph Theory.

[4] Wilfried Imrich. Über das schwache kartesische Produkt von Graphen , 1971 .

[5] Alexander Russell,et al. A Note on the Asymptotics and Computational Complexity of Graph Distinguishability , 1998, Electron. J. Comb..

[6] Xuding Zhu,et al. Cartesian powers of graphs can be distinguished by two labels , 2007, Eur. J. Comb..

[7] Michael O. Albertson,et al. Symmetry Breaking in Graphs , 1996, Electron. J. Comb..

[8] Donald J. Miller. Weak cartesian product of graphs , 1970 .

[9] Donald J. Miller. The automorphism group of a product of graphs , 1970 .

[10] Wilfried Imrich,et al. The distinguishing number of Cartesian products of complete graphs , 2008, Eur. J. Comb..

[11] W. Imrich,et al. Handbook of Product Graphs, Second Edition , 2011 .

[12] Wilfried Imrich,et al. Distinguishing Infinite Graphs , 2007, Electron. J. Comb..

[13] Gert Sabidussi,et al. Graph multiplication , 1959 .