The Zero Divisor Graph of the Ring Z_(2^2 p)

Nazar H. Shuker, Payman A. Rashed

Abstract


In this paper, we consider the crossing number and the chromatic number of the zero divisor graph Γ(Z_(2^2 p)) to show that this type of zero divisor graphs is bipartite graph, and the smallest cycle in Γ(Z_(2^2 p)) is of length four this implies that the girth is equal four.


Keywords


Bipartite graph, crossing number, girth, planar graph, zero divisor graph of the ring Z_(2^2 p).

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References


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DOI: http://dx.doi.org/10.14500/aro.10058
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Copyright (c) 2016 Nazar H. Shuker, Payman A. Rashed

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