On The Strong Metric Dimension of Generalized Petersen Graph GP_{n,1} and K_m \odot P_n Graph Nafis Saiful Arsyi (a*), Tri Atmojo Kusmayadi (a)
a) Faculty of Mathematics and Natural Sciences, Sebelas Maret University
Jalan Ir. Sutami No. 36 Kentingan, Jebres Surakarta 57126, Indonesia
*nafisarsyi16[at]student.uns.ac.id
Abstract
Let G be a connected graph with vertex set V(G) and edge set E(G). For every pair of vertices u and v in V(G), the interval I[u,v] between vertex u and vertex v is the collection off all vertices that belong to some shortest u - v path. A vertex s in set S where S is subset of V(G) strongly resolves two vertices u and v if u belongs to a shortest v - s path or if v belongs to a shortest u - s path. A vertex set S of G is a strong resolving set of G if every two distinct vertices in G are strongly resolved by some vertex in set S. The strong resolving set of G with minimal cardinality is defined as strong metric basis and the strong metric dimension sdim(G) of a graph G is defined as the cardinality of strong metric basis. In this research we determine the strong dimension metric of complete graph with corona operation by path graph and generalized petersen GP_{n,1} graph with n\geq 3. The method thst used in this research is literature study. We obtain the strong metric dimension of complete graph with corona operation by path graph is sdim(K_m \odot P_n) = m for m \geq 3 and n=1, and sdim(K_m \odot P_n) = 2m for m \geq 3 and n \geq 2. The strong dimension of generalized Petersen graph GP_{n,1} is sdim(GP_{n,1} ) = n for n\geq 3.
