Zero Forcing Number of Cubic and Quartic Cayley Graphs on Abelian Groups

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Let [Formula: see text] be the Cayley graph on the abelian group [Formula: see text]. The zero forcing number [Formula: see text] of graph [Formula: see text] is the minimum of [Formula: see text] over all zero forcing sets [Formula: see text]. In this paper, for cubic connected Cayley graphs [Formula: see text] on abelian groups [Formula: see text], we show that [Formula: see text] or [Formula: see text]. Moreover, we prove that for quartic connected Cayley graphs [Formula: see text] on abelian groups [Formula: see text] with [Formula: see text], either [Formula: see text] or [Formula: see text] is determined by the order of the elements of [Formula: see text].