Glasnik Matematicki, Vol. 49, No. 2 (2014), 263-273.

THE GRAPH OF EQUIVALENCE CLASSES OF ZERO-DIVISORS OF A POSET

Hongxing Liu

School of Mathematical Sciences, Shandong Normal University, 250014 Jinan, P. R. China
e-mail: lhxshanda@163.com


Abstract.   In this paper, we give the definition of the graph of equivalence classes of zero-divisors of a poset P. We prove that if [a] has maximal degree in V(γE(P)), then ann(a) is maximal in Anih(P). Also, we give some other properties of the graph γE(P). Moreover, we characterize the cut vertices of γE(P) and study the cliques of these graphs.

2010 Mathematics Subject Classification.   05E99, 06A07.

Key words and phrases.   Zero-divisor graph, poset, cut vertex, equivalence class, clique.


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DOI: 10.3336/gm.49.2.02


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