ON THE STRONG METRIC DIMENSION OF A LOLLIPOP
GRAPH, A GENERALIZED WEB GRAPH, AND A
GENERALIZED FLOWER GRAPH
Tiffani Arzaqi Putri and Tri Atmojo Kusmayadi
Department of Mathematics
Faculty of Mathematics and Natural Sciences
Sebelas Maret University
Abstract. Let G be a connected graph with vertex set V (G) and edge set E(G). The
interval I[u; v] between u and v to be the collection of all vertices that belong to some
shortest u − v path. A vertex s strongly resolves two vertices u and v if u belongs to a
shortest v − s path, denoted by u ∈ I[v; s] or v belongs to a shortest u − s path, denoted
by v ∈ I[u; s]. A vertex set S of G is a strong resolving set of G if every two distinct
vertices of G are strongly resolved by some vertex of S. The strong metric basis of G is a
strong resolving set with minimal cardinality. The strong metric dimension sdim(G) of a
graph G is de ned as the cardinality of strong metric basis. In this paper we determine
the strong metric dimension of lollipop Lm;n graph, generalized web WB(G; m; n) graph,
and generalized
ower FL(G; m; n; p) graph.
Keywords : strong metric dimension, strong resolving, lollipop graph, generalized web
graph, generalized
ower graph
1.
