Domination in graphs has applications to several fields. A similar problem occurs when the maximum distance to a facility is fixed and one attempts to minimize the no of facilities necessary so that everyone is serviced. The prominence of Circular-arc graphs in the current times is evident from the enhanced research focus and attempts for extensive exploration during the recent years. In this paper, we derived the some properties on sum of degrees of elements in a minimum dominating set through the quotient of divisor 3, domination number and the number of vertices of the circular-arc graphs corresponding to a circular-arc family in a particular case of each arc intersects the next arc only by using Euclidean division lemma.
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