The Edge Metric Dimension of Comb Product Cycles Versus Stars and Fans

Abstract

The edge metric dimension finding of a graph resulting from the comb product on a cycle graph to the complete graph and the fact about the dominant vertex in the complete graph arise a problem about the edge metric dimension of a graph resulting from the comb product on a cycle graph to the other graphs that have dominant vertex such as star and fan graph. This study aims to determine the edge metric dimension of the graph resulting from the comb product on a cycle graph to the star and fan graph, respectively. The results show that the upper and lower bound of the edge metric dimension of both graphs are equivalent so that an exact edge metric dimension is obtained. The edge metric dimension of the graph comb product of the cycle graph C_n to the star graph S_(1,m) is n(m-1). The edge metric dimension of the graph comb product of the cycle graph C_n to the fan graph F_(1,m) is n(m-1).

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