The partition dimension of cycle books graph

Jaya Santoso, Darmaji

Research output: Contribution to journalConference articlepeer-review

9 Citations (Scopus)


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 ∏ = {S1, S2, S3,..., Sk } of V(G), the representation of v with respect to ∏ is defined by r(v|∏) = (d(v, S1), d(v, S2),..., d(v, Sk )). 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 Cr with the common path P2. 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 languageEnglish
Article number012070
JournalJournal of Physics: Conference Series
Issue number1
Publication statusPublished - 22 Mar 2018
Event3rd International Conference on Mathematics: Pure, Applied and Computation, ICoMPAC 2017 - Surabaya, Indonesia
Duration: 1 Nov 20171 Nov 2017


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