## Abstract

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 + 2k for m = 3k + 2, 4 + 2(k - 1) for m = 3k + 1, and 3 + 2(k - 1) for m = 3k. is m + 1.

Original language | English |
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Article number | 012070 |

Journal | Journal of Physics: Conference Series |

Volume | 974 |

Issue number | 1 |

DOIs | |

Publication status | Published - 22 Mar 2018 |

Event | 3rd International Conference on Mathematics: Pure, Applied and Computation, ICoMPAC 2017 - Surabaya, Indonesia Duration: 1 Nov 2017 → 1 Nov 2017 |