The partition dimension of cycle books graph
Jaya Santoso, Darmaji · Journal of Physics Conference Series · 2018
Let G be a nontrivial and connected graph with vertex set V ( G ), edge set E ( G ) and S ⊆ V ( G ) with v ∈ V ( G ), the distance between v and S is d ( v , S ) = min { d ( v , x )| x ∈ S }. For an ordered partition ∏ = { S 1 , S 2 , S 3 ,..., S k } of V ( G ), the representation of v with respect to ∏ is defined by r ( v |∏) = ( d ( v , S 1 ), d ( v , S 2 ),..., d ( v , S k )). The partition ∏ is called a resolving partition of G if all representations of vertices are distinct. The partition dimension pd ( G ) is the smallest integer k such that G has a resolving partition set with k members. In this research, we will determine the partition dimension of Cycle Books . Cycle books graph is a graph consisting of m copies cycle C r with the common path P 2 . It is shown that the partition dimension of cycle books graph, is 3 for m = 2, 3, and m for m ≥ 4. is 3 + 2 k for m = 3 k + 2, 4 + 2( k − 1) for m = 3 k + 1, and 3 + 2( k − 1) for m = 3 k . is m + 1.