The Edge Metric Dimension of the Comb Product of a Cycle and a Graph with a Dominant Vertex

Mn, Abdilla Nurul Azisah (Hasanuddin University)
Hasmawati, Hasmawati (Hasanuddin University)
Nurwahyu, Budi (Hasanuddin University)
Hinding, Nurdin (Hasanuddin University)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 14, No 1 (2026): Electronic Journal of Graph Theory and Applications

In this paper, we determine the edge metric dimension of the comb product of a cycle graph and a simple graph containing a dominant vertex. This result generalizes previous findings on the edge metric dimension of the comb product of a cycle and a complete graph. We show that the edge metric dimension of Cn ▷ D, where D is a simple graph with a dominant vertex, equals the product of the order of Cn and the order of D reduced by two.