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

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

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.

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Veröffentlicht in:ARO (Koya) 2016-12, Vol.4 (2), p.47-50
Hauptverfasser: Shuker, Nazar, Rashed, Payman
Format: Artikel
Sprache:eng
Schlagworte:
bipartite graph, crossing number, girth, planar graph, zero divisor graph of the ring z_(2^2 p)
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Zusammenfassung: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.
ISSN:2410-9355
2307-549X
DOI:10.14500/aro.10058