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- W2740184966 abstract "For a vertex v of a connected graph G(V, E) with vertex set V(G), edge set E(G) and S ⊆ V(G). Given an ordered partition Π = {S1, S2, S3, …, Sk} of the vertex set V of G, the representation of a vertex v ∈ V with respect to Π is the vector r(v|Π) = (d(v, S1), d(v, S2), …, d(v, Sk)), where d(v, Sk) represents the distance between the vertex v and the set Sk and d(v, Sk) = min{d(v, x)|x ∈ Sk}. A partition Π of V(G) is a resolving partition if different vertices of G have distinct representations, i.e., for every pair of vertices u, v ∈ V(G), r(u|Π) ≠ r(v|Π). The minimum k of Π resolving partition is a partition dimension of G, denoted by pd(G). Finding the partition dimension of G is classified to be a NP-Hard problem. In this paper, we will show that the partition dimension of comb product of path and complete graph. The results show that comb product of complete grapph Km and path Pn namely pd(Km⊳Pn)=m where m ≥ 3 and n ≥ 2 and pd(Pn⊳Km)=m where m ≥ 3, n ≥ 2 and m ≥ n." @default.
- W2740184966 created "2017-08-08" @default.
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- W2740184966 date "2017-01-01" @default.
- W2740184966 modified "2023-10-09" @default.
- W2740184966 title "On the partition dimension of comb product of path and complete graph" @default.
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- W2740184966 doi "https://doi.org/10.1063/1.4994441" @default.
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