Abstract
The distance d(z1, z2) from vertex z1 ∈ V(G) to z2 ∈ V(G) is minimum length of (z1, z2)‐path in a given connected graph G having E(G) and V(G) edges and vertices’/nodes’ sets, respectively. Suppose Z = {z1, z2, z3, …, zm}⊆V(G) is an order set and c ∈ V(G), and the code of c with reference to Z is the m‐tuple {d(c, z1), d(c, z2), d(c, z13), …, d(c, zk)}. Then, Z is named as the locating set or resolving set if each node of G has unique code. A locating set of least cardinality is described as a basis set for the graph G, and its cardinal number is referred to as metric dimension symbolized by dim(G). Metric dimension of certain subdivided convex polytopes STn has been computed, and it is concluded that just four vertices are sufficient for unique coding of all nodes belonging to this family of convex polytopes.
Highlights
Metric dimension of certain subdivided convex polytopes STn has been computed, and it is concluded that just four vertices are sufficient for unique coding of all nodes belonging to this family of convex polytopes
In the discipline of computer science and mathematics, graph theory [1] is the survey of graphs that considers the link between edges and vertices. is is the most celebrated discipline these days that has applications [2] in computer science, information technology, biosciences, mathematics, social sciences, physics, chemistry, and linguistics
Convex polytopes are the principal geometric structures which are under investigation since antiquity. e charm of this concept is nowadays complemented by their significance for various mathematical fields, extending from algebraic geometry, linear programming, integration, and combinatorial optimization
Summary
E distance d(z1, z2) from vertex z1 ∈ V(G) to z2 ∈ V(G) is minimum length of (z1, z2)-path in a given connected graph G having E(G) and V(G) edges and vertices’/nodes’ sets, respectively. Zm⊆V(G) is an order set and c ∈ V(G), and the code of c with reference to Z is the m-tuple {d(c, z1), d(c, z2), d(c, z13), . En, Z is named as the locating set or resolving set if each node of G has unique code. A locating set of least cardinality is described as a basis set for the graph G, and its cardinal number is referred to as metric dimension symbolized by dim(G). Metric dimension of certain subdivided convex polytopes STn has been computed, and it is concluded that just four vertices are sufficient for unique coding of all nodes belonging to this family of convex polytopes
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